บทเรีบนโปรแกรม ชุดที่ 39

กรอบที่ 7 คาชีแ้ จง : เติมเครอ่ื งหมาย , x ลงใน………ให้ถูกต้อง ตวั อยา่ ง 1. ……x…… (x+ 1)2 เปน็ ตัวประกอบของ x2 +2x+2 2. ………… -7 และ 2 เปน็ คาตอบของสมการ 3x2 + 19x- 14 1. ………… -6 และ 8 เป็นคาตอบของสมการ x2 -2x- 48 2. ………… -2 และ 5 เปน็ คาตอบของสมการ x2 -3x+ 10 3. ………… (x-3)(3x+3) เปน็ ตวั ประกอบของ 3x2 -6x- 9 = 0 4. ………… (4x+7)(3x-5) เปน็ ตวั ประกอบของ -12x2 - x+35 = 0 5. ………… -4 และ 13 เป็นคาตอบของสมการ x2 - 9x-52 6. ………… (13+ x)(5- x) เปน็ ตัวประกอบของ 65+8x- x2 = 0 7. ………… - 1 และ 3 เป็นคาตอบของสมการ 6x2 -7x-3 3 2 8. ………… - 1 และ 9 เป็นคาตอบของสมการ 4x2 + 16x – 9 2 2 9. ………… (3x – 2)(4x – 5) เปน็ ตัวประกอบของ 12x2 -23x+ 10 10. ………… - 1 และ -1 เป็นคาตอบของสมการ 5x2 + 4x – 1 2

คาชี้แจง : เติมเครื่องหมาย , x ลงใน………ให้ถกู ตอ้ ง ตัวอย่าง 1. ……x…… (x+ 1)2 เปน็ ตวั ประกอบของ x2 +2x+2 2. ………… -7 และ 2 เปน็ คาตอบของสมการ 3x2 + 19x- 14 1. ………… -6 และ 8 เป็นคาตอบของสมการ x2 -2x- 48 2. ………… -2 และ 5 เปน็ คาตอบของสมการ x2 -3x+ 10 3. ………… (x-3)(3x+3) เปน็ ตัวประกอบของ 3x2 -6x- 9 = 0 4. ……x…… (4x+7)(3x-5) เปน็ ตัวประกอบของ -12x2 - x+35 = 0 5. ………… -4 และ 13 เปน็ คาตอบของสมการ x2 - 9x-52 6. ……x…… (13+ x)(5- x) เปน็ ตวั ประกอบของ 65+8x- x2 = 0 7. ………… - 1 และ 3 เปน็ คาตอบของสมการ 6x2 -7x-3 3 2 8. ……x…… - 1 และ 9 เปน็ คาตอบของสมการ 4x2 + 16x – 9 2 2 9. ………… (3x – 2)(4x – 5) เปน็ ตวั ประกอบของ 12x2 -23x+ 10 10. ……x…… - 1 และ -1 เปน็ คาตอบของสมการ 5x2 + 4x – 1 2

กรอบท่ี 8 คาช้แี จง : ใหน้ ักเรยี นแสดงวธิ ที าให้ถกู ตอ้ ง ตวั อยา่ งที่ จงหาคาตอบของสมการ 3x2 +2x-5 = 0 .......ว.ธิ..ีท..า............3.x..2.+...2.x...-....5...=...0................................................................. .......................................(..3..x...+...5...).(...x...-...1..)...=...0........................................ ..............................(..3..x...+...5...)..=....0...ห..ร.ือ...(..x...-....1..)...=...0................................... .......ใ..ห..้ ....3..x...+...5....=....0..................................ใ.ห..้.....x...-...1..=....0......................... .......จ.ะ..ไ.ด..้ .3..x...+...5...+...(.-.5..)...=...0...+...(.-..5.).................จ.ะ.ไ..ด..้ .x...-...1..+...1...=...0...+...1............... ............................................................−.........53......x............3...13...x...x......==...=......(...-...−−5...3...5...5...)............31.........................................................................................................x.........=............1............................................................... ........ด..ัง..น.้นั.........3......แ.ล..ะ....1....เ.ป..น็ ..ค.า.ต..อ..บ..ข.อ..ง.ส.ม..ก..า.ร................................................ ....................................แจ...ะท...ไ...น...ด......้ ...x......3...ด...ว้......ย−...3...5............2...−...+3...52...354......ใ...−น......−ส...3...5ม2...30...ก...า...--ร.........55...ต......ร==...ว...จ......00ค...า......ต...อ......บ................................................................................................................................................ ..................................................0...=...0...................................................... ............แ.ท..น....x...ด.ว้..ย...1..ใ..น..ส.ม..ก..า.ร...................................................................... .............จ.ะ..ไ.ด..้ .3..(..1...).2.+...2..(..1...)..-...5...=....0........................................................... ................................3...+...2...-...5...=....0........................................................... ............................................0...=....0........................................................... ........ด..ัง.น..ัน้ .......−.3.5.....แ..ล.ะ.....1....เป..็น..ค..า.ต..อ.บ..ข..อ.ง.ส..ม..ก.า..ร................................................

ข้อที่ 1 จงหาคาตอบของสมการ x2 -14x+45 = 0 ....ว.ิธ..ีท..า..................................................................................................... .............................................................................................................. .............................................................................................................. .............................................................................................................. .............................................................................................................. .............................................................................................................. .............................................................................................................. .............................................................................................................. .............................................................................................................. ตรวจคาตอบ .............................................................................................................. .............................................................................................................. .............................................................................................................. .............................................................................................................. .............................................................................................................. .............................................................................................................. .............................................................................................................. .............................................................................................................. ..............................................................................................................

ขอ้ ท่ี 2 จงหาคาตอบของสมการ x2 -4x-21 = 0 ....ว.ิธ..ที ..า..................................................................................................... .............................................................................................................. .............................................................................................................. .............................................................................................................. .............................................................................................................. .............................................................................................................. .............................................................................................................. .............................................................................................................. .............................................................................................................. ตรวจคาตอบ .............................................................................................................. .............................................................................................................. .............................................................................................................. .............................................................................................................. .............................................................................................................. .............................................................................................................. .............................................................................................................. .............................................................................................................. ..............................................................................................................

ขอ้ ท่ี 3 จงหาคาตอบของสมการ 3x2 -x-24 = 0 ....ว.ธิ..ที ..า..................................................................................................... .............................................................................................................. .............................................................................................................. .............................................................................................................. .............................................................................................................. .............................................................................................................. .............................................................................................................. .............................................................................................................. .............................................................................................................. ตรวจคาตอบ .............................................................................................................. .............................................................................................................. .............................................................................................................. .............................................................................................................. .............................................................................................................. .............................................................................................................. .............................................................................................................. .............................................................................................................. ..............................................................................................................

ขอ้ ที่ 4 จงหาคาตอบของสมการ 6x2 + 7x + 2 = 0 ....ว.ิธ..ที ..า..................................................................................................... .............................................................................................................. .............................................................................................................. .............................................................................................................. .............................................................................................................. .............................................................................................................. .............................................................................................................. .............................................................................................................. .............................................................................................................. ตรวจคาตอบ .............................................................................................................. .............................................................................................................. .............................................................................................................. .............................................................................................................. .............................................................................................................. .............................................................................................................. .............................................................................................................. .............................................................................................................. ..............................................................................................................

ขอ้ ที่ 5 จงหาคาตอบของสมการ 8x2 - 2x – 3 = 0 ....ว.ิธ..ที ..า..................................................................................................... .............................................................................................................. .............................................................................................................. .............................................................................................................. .............................................................................................................. .............................................................................................................. .............................................................................................................. .............................................................................................................. .............................................................................................................. ตรวจคาตอบ .............................................................................................................. .............................................................................................................. .............................................................................................................. .............................................................................................................. .............................................................................................................. .............................................................................................................. .............................................................................................................. .............................................................................................................. ..............................................................................................................

คาชี้แจง : ให้นกั เรยี นแสดงวิธที าใหถ้ กู ตอ้ ง ตัวอย่างท่ี จงหาคาตอบของสมการ 3x2 +2x-5 = 0 .......ว.ิธ..ีท..า............3.x..2.+...2.x...-....5...=...0................................................................. .......................................(..3..x...+...5...).(...x...-...1..)...=...0........................................ ..............................(..3..x...+...5...)..=....0...ห..ร.ือ...(..x...-....1..)...=...0................................... .......ใ..ห..้ ....3..x...+...5....=....0..................................ใ.ห..้.....x...-...1..=....0......................... .......จ.ะ..ไ.ด..้ .3..x...+...5...+...(.-.5..)...=...0...+...(.-..5.).................จ.ะ.ไ..ด..้ .x...-...1..+...1...=...0...+...1............... ............................................................−.........53......x............3...13...x...x......==...=......(...-...−−5...3...5...5...)............31.........................................................................................................x.........=............1............................................................... ........ด..งั..น.น้ั.........3......แ.ล..ะ....1....เ.ป..็น..ค.า.ต..อ..บ..ข.อ..ง.ส.ม..ก..า.ร................................................ ....................................แจ...ะท...ไ...น...ด......้ ...x......3...ด...ว้......ย−...3...5............2...−...+3...52...354......ใ...−น......−ส...3...5ม2...30...ก...า...--ร.........55...ต......ร==...ว...จ......00ค...า......ต...อ......บ................................................................................................................................................ ..................................................0...=...0...................................................... ............แ.ท..น....x...ด.ว้..ย...1..ใ..น..ส.ม..ก..า.ร...................................................................... .............จ.ะ..ไ.ด..้ .3..(..1...).2.+...2..(..1...)..-...5...=....0........................................................... ................................3...+...2...-...5...=....0........................................................... ............................................0...=....0........................................................... ........ด..ัง.น..้นั .......−.3.5.....แ..ล.ะ.....1....เป..็น..ค..า.ต..อ.บ..ข..อ.ง.ส..ม..ก.า..ร................................................

ขอ้ ที่ 1 จงหาคาตอบของสมการ x2 -14x+45 = 0 ....ว.ิธ..ีท..า...............x.2...-...1.4..x...+...4.5....=...0.............................................................. .......................................(...x...-...5...).(..x...-....9..)...=...0......................................... ................................(..x...-...5....)..=....0...ห..ร.ือ...(..x...-...9...)...=...0.................................. .......ใ.ห..้.....x...-...5.....=...0....................................ใ..ห.้.....x...-...9...=...0......................... .......จ.ะ.ไ..ด..้ .x...-...5...+...5...=....0...+...5..........................จ.ะ..ไ.ด..้ .x...-...9...+...9...=...0...+...9.............. ..........................x...=...5....................................................x...=...9.................... .............................................................................................................. .............................................................................................................. ....ด.งั..น..นั้ ......5.....แ..ล.ะ.....9....เ.ป..น็ ..ค.า.ต..อ..บ..ข.อ..ง.ส.ม..ก..า.ร....................................................... ตรวจคาตอบ ......แ..ท..น....x.....ด..้ว.ย.....5....ใ..น..ส.ม..ก..า.ร..................................................................... ......จ.ะ..ไ.ด..้ ...5.2..–...1.4.(...4...)...+...4.5....=...0................................................................... .....................1.0...–...5..6...+.4..5...=....0................................................................... .....................................0...=...0................................................................... ......แ..ท..น...x...ด..ว้ .ย.....1...ใ..น..ส.ม..ก..า.ร......................................................................... .......จ..ะ.ไ.ด..้ ...9.2...-...1.4..(...9..)...+...4.5....=...0................................................................. .....................8..1...-...12..6...+...4.5....=...0................................................................. ......................................0...=....0................................................................. ....ด..ัง.น..ั้น.......5.....แ.ล..ะ....9.....เป..็น..ค..า.ต..อ.บ..ข..อ.ง.ส..ม..ก.า..ร......................................................

ขอ้ ที่ 2 จงหาคาตอบของสมการ x2 -4x-21 = 0 ....ว.ธิ..ที ..า...............x.2...-...4..x...-...2..1..=...0................................................................ .......................................(...x...+..3...).(...x...-...7...)...=...0......................................... ................................(..x...+...3...)...=...0...ห..ร.ือ...(...x...-...7...)...=...0.................................. .......ใ.ห..้.....x...+...3....=....0....................................ใ..ห.้.....x...-...7...=...0......................... .......จ.ะ.ไ..ด..้ .x...+...3.(..-.3..)..=....0...+...(.-.3..).......................จ.ะ..ไ.ด..้ .x...-...7...+...7...=....0...+...7............. .........................x...=....-.3...................................................x...=...7.................... .............................................................................................................. .............................................................................................................. ....ด.งั..น..ัน้ ......-..3.....แ.ล..ะ....7....เ.ป..น็..ค..า.ต..อ.บ..ข..อ.ง.ส..ม..ก.า..ร..................................................... ตรวจคาตอบ ......แ..ท..น....x.....ด..้ว.ย.....-.3.....ใ.น..ส..ม.ก..า.ร.................................................................... ......จ.ะ..ไ.ด..้ ...(.-.3..).2..–...4.(.-..3.)...-...2.1...=...0................................................................... ........................9..+...1.2...-...2.1...=...0................................................................... .....................................0...=...0................................................................... ......แ..ท..น...x...ด..้ว.ย.....7....ใ..น..ส.ม..ก..า.ร........................................................................ .......จ..ะ.ไ.ด..้ ...7.2....-...4.(...7...)...-...2.1..=....0.................................................................. .....................4..9...-...2.8....-...2.1..=....0.................................................................. ......................................0...=....0................................................................. ....ด..ัง.น..น้ั .......-..3....แ..ล.ะ.....7....เ.ป..น็ ..ค.า..ต.อ..บ..ข.อ..ง.ส..ม.ก..า.ร.....................................................

ขอ้ ท่ี 3 จงหาคาตอบของสมการ 3x2 -x-24 = 0 ....ว.ิธ..ที ..า.............3..x.2...-...x...-...2..4...=...0................................................................. ......................................(...3.x...+...8...).(...x...-...3...)..=....0........................................ ...............................(...3.x...+...8...)...=...0...ห..ร.อื...(...x...-...3...)...=...0................................. .......ใ.ห..้.....3.x...+...8.....=...0...................................ใ..ห.้.....x...-...3...=...0......................... .......จ.ะ.ไ..ด..้ .3..x...+..8....+..(..-.8..)..=....0...+...(.-.8..).................จ.ะ..ไ.ด..้ .x...-...3...+...3...=....0...+..3.............. ..............................3.x...=....-.8.............................................x...=...3.................... ........................3..x....31....=...(.−.−.8.8.)....31................................................................ ...............−..8...............x...=.....3...................................................................... ....ด.ัง..น..้ัน.......3.....แ..ล..ะ....3....เ.ป..็น..ค..า.ต..อ.บ..ข..อ.ง.ส..ม..ก.า.ร...................................................... −8 ตรวจคาตอบ ..................แจ...ะ...ท...ไ...นด......้ ......3x............−...ด3...8...ว้ ...ย......2...−...1...99...32......−...+3...8...ใ...83น......ส...--...ม...ก...22...า44...ร......=...=.........00.......................................................................................................................................................................................... .........................................0....=...0.............................................................. ......แ..ท..น...x...ด..้ว.ย.....3....ใ..น.ส..ม..ก.า..ร........................................................................ .......จ..ะ.ไ.ด..้ ...3.(...3...).2...-...3...-...2..4...=...0.................................................................. .......................2.7...-...3...-...2..4...=...0.................................................................. ...............−..8.....................0...=....0................................................................. ....ด..ัง.น..้นั.......3......แ..ล.ะ....3.....เ.ป..น็ ..ค.า.ต..อ..บ..ข.อ..ง.ส.ม..ก..า.ร.....................................................

ขอ้ ท่ี 4 จงหาคาตอบของสมการ 6x2 + 7x + 2 = 0 ....ว.ธิ..ีท..า.............6..x.2...+...7..x...+..2...=....0................................................................. .....................................(...2.x...+...1..)..(..3..x...+...2..)...=...0......................................... ...............................(...2.x...+...1..)...=...0....ห.ร..อื ...(..3..x...+...2..)...=...0................................. .......ใ.ห..้.....2.x...+...1....=...0....................................ใ..ห.้.....3.x...+...2...=....0....................... .......จ.ะ.ไ..ด..้ .2..x...+..1...+...(.-.1.)...=...0...+...(.-..1.)...................จ.ะ..ไ.ด..้ .3..x...+...2...+..(.-..2.)...=...0....+..(..-.2..).... ............................2..x...=...-..1..................................................3.x....=...-.2............. ......................2..x....21.....=...(.−−..11.)....21.......................................3.x....31.....=..(..−.−.2.2)....31...... ..............................x...=....2.....................................................x...=......3........... ....ด.งั..น..ั้น.......−.2.1...แ..ล..ะ....−.3.2....เ.ป..น็ ..ค.า.ต..อ.บ..ข..อ.ง..ส.ม..ก..า.ร.................................................... ตรวจคาตอบ ..................แจ...ะ...ท...ไ...นด......้ ......x...6............ด−...2...ว้1...ย23......2...++......7−...2......1−...−2...2...ใ71...น......ส...++...ม...ก...22...า...ร...==.........00................................................................................................................................................................................................ ..........................−...2...........0...=...0................................................................ ..................แจ...ะ...ทไ......นด......้ ......x6............−...ด3...2...ว้ 83...ย......2...++......73.........−...−3...13...ใ42...น......ส...++...ม...ก...22...า...ร...==.........00................................................................................................................................................................................................ ........................................0...=...0................................................................ ....ด..งั .น..้นั ........−.2.1...แ..ล.ะ.....−.3.2...เ.ป..็น..ค..า.ต..อ.บ..ข..อ.ง.ส..ม..ก.า..ร...................................................

ข้อท่ี 5 จงหาคาตอบของสมการ 8x2 - 2x – 3 = 0 ....ว.ิธ..ีท..า.............8..x.2...-...2..x...-...3...=...0................................................................. .....................................(...2.x...+...1..)..(..4..x...-...3...)..=....0........................................ ...............................(...2.x...+...1..)...=...0....ห.ร..ือ...(..4..x...-...3...)...=...0................................ .......ใ.ห..้.....2.x...+...1....=...0....................................ใ..ห.้.....4..x...-...3...=...0....................... .......จ.ะ.ไ..ด..้ .2..x...+..1...+...(.-.1.)...=...0...+...(.-..1.)...................จ.ะ..ไ.ด..้ ....4..x...-...3...+...3...=...0...+...3......... ............................2..x...=...-..1..................................................4..x...=...3.............. ......................2..x....21.....=...(.−−..11.)....21......................................4..x....41.....=...(.3..3)....41....... ........ด..งั....น....้ัน..............−..2..1......แ....ล....ะ........43..x......=เ..ป....็น..2..ค....า..ต....อ..บ....ข..อ....ง..ส....ม....ก..า..ร....................................................................x......=............4...................... ตรวจคาตอบ ............แจ..ะ..ท..ไ..นด....้ ....x..8........ด−..2..้ว1..ย....2..-....−..22....1..−..2..ใ1..น....ส..-..ม..ก..3..า..ร..=......0................................................................................................................................ .............................2...+...1..-...3...=...0................................................................ ...........................3.............0...=...0................................................................ ..................แจ...ะ...ทไ......นด......้ ......x......8.........ด...43...ว้ ...ย......2...-...14...482......-......ใ43......46น...ส...--...ม......ก33...า......ร==............00................................................................................................................................................................................................... ........ด....ัง..น....นั้................−..2..1......แ....ล..ะ..........43........เ..ป....น็ ....ค0..า..ต..=..อ....บ0....ข..อ....ง..ส..ม....ก....า..ร..........................................................................................................

ขอแสดงความยนิ ดีกับนักเรยี นทตี่ อบ ถูกด้วยนะคะ แตส่ าหรบั นกั เรยี นที่ตอบไมถ่ ูก ไมต่ อ้ งเสียใจ ลองกลับไปทบทวนใหม่ อกี คร้งั แล้วคุณครูเชอ่ื วา่ นักเรยี นจะตอ้ งทา ได้อย่างแน่นอนค่ะ ขอบคุณคะ่ / ครบั คณุ ครู

กลุม่ สาระการเรียนรคู้ ณติ ศาสตร์ ชน้ั มัธยมศกึ ษาปีท่ี 2 ดีกรสี อง บทเรยี นโปรแกรม เร่ือง การหาคาตอบของสมการ ax2 + bx + c = 0 โดยการแยกตัวประกอบ จดั ทาโดย นางสาวสุธิดา เปง็ เรอื น รหัส 601120056 Section : AB คณะครศุ าสตร์ วชิ าเอกคณติ ศาสตร์ เสนอ ผู้ชว่ ยศาสตราจารย์มนู สมเพชร