一元二次方程练习题 含答案.docx
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一元二次方程练习题 含答案.docx
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一元二次方程练习题含答案
经典解法20题
(1)(3x+1)^2=7
(2)9x^2-24x+16=11
(3)(x+3)(x-6)=-8
(4)2x^2+3x=0
(5)6x^2+5x-50=0(选学)
(6)x^2-4x+4=0(选学)
(7)(x-2)^2=4(2x+3)^2
(8)y^2+2√2y-4=0
(9)(x+1)^2-3(x+1)+2=0
(10)x^2+2ax-3a^2=0(a为常数)
(11)2x^2+7x=4.
(12)x^2-1=2x
(13)x^2+6x+5=0
(14)x^2-4x+3=0
(15)7x^2-4x-3=0
(16)x^2-6x+9=0
(17)x²+8x+16=9
(18)(x²-5)²=16
(19)x(x+2)=x(3-x)+1
(20)6x^2+x-2=0
海量111题
1)x^2-9x+8=0
(2)x^2+6x-27=0
(3)x^2-2x-80=0
(4)x^2+10x-200=0
(5)x^2-20x+96=0
(6)x^2+23x+76=0
(7)x^2-25x+154=0
(8)x^2-12x-108=0
(9)x^2+4x-252=0
(10)x^2-11x-102=0
(11)x^2+15x-54=0
(12)x^2+11x+18=0
(13)x^2-9x+20=0
(14)x^2+19x+90=0
(15)x^2-25x+156=0
(16)x^2-22x+57=0
(17)x^2-5x-176=0
(18)x^2-26x+133=0
(19)x^2+10x-11=0
(20)x^2-3x-304=0
(21)x^2+13x-140=0
(22)x^2+13x-48=0
(23)x^2+5x-176=0
(24)x^2+28x+171=0
(25)x^2+14x+45=0
(26)x^2-9x-136=0
(27)x^2-15x-76=0
(28)x^2+23x+126=0
(29)x^2+9x-70=0
(30)x^2-1x-56=0
(31)x^2+7x-60=0
(32)x^2+10x-39=0
(33)x^2+19x+34=0
(34)x^2-6x-160=0
(35)x^2-6x-55=0
(36)x^2-7x-144=0
(37)x^2+20x+51=0
(38)x^2-9x+14=0
(39)x^2-29x+208=0
(40)x^2+19x-20=0
(41)x^2-13x-48=0
(42)x^2+10x+24=0
(43)x^2+28x+180=0
(44)x^2-8x-209=0
(45)x^2+23x+90=0
(46)x^2+7x+6=0
(47)x^2+16x+28=0
(48)x^2+5x-50=0
(49)x^2+13x-14=0
(50)x^2-23x+102=0
(51)x^2+5x-176=0
(52)x^2-8x-20=0
(53)x^2-16x+39=0
(54)x^2+32x+240=0
(55)x^2+34x+288=0
(56)x^2+22x+105=0
(57)x^2+19x-20=0
(58)x^2-7x+6=0
(59)x^2+4x-221=0
(60)x^2+6x-91=0
(61)x^2+8x+12=0
(62)x^2+7x-120=0
(63)x^2-18x+17=0
(64)x^2+7x-170=0
(65)x^2+6x+8=0
(66)x^2+13x+12=0
(67)x^2+24x+119=0
(68)x^2+11x-42=0
(69)x^20x-289=0
(70)x^2+13x+30=0
(71)x^2-24x+140=0
(72)x^2+4x-60=0
(73)x^2+27x+170=0
(74)x^2+27x+152=0
(75)x^2-2x-99=0
(76)x^2+12x+11=0
(77)x^2+17x+70=0
(78)x^2+20x+19=0
(79)x^2-2x-168=0
(80)x^2-13x+30=0
(81)x^2-10x-119=0
(82)x^2+16x-17=0
(83)x^2-1x-20=0
(84)x^2-2x-288=0
(85)x^2-20x+64=0
(86)x^2+22x+105=0
(87)x^2+13x+12=0
(88)x^2-4x-285=0
(89)x^2+26x+133=0
(90)x^2-17x+16=0
(91)x^2+3x-4=0
(92)x^2-14x+48=0
(93)x^2-12x-133=0
(94)x^2+5x+4=0
(95)x^2+6x-91=0
(96)x^2+3x-4=0
(97)x^2-13x+12=0
(98)x^2+7x-44=0
(99)x^2-6x-7=0
(100)x^2-9x-90=0
(101)x^2+17x+72=0
(102)x^2+13x-14=0
(103)x^2+9x-36=0
(104)x^2-9x-90=0
(105)x^2+14x+13=0
(106)x^2-16x+63=0
(107)x^2-15x+44=0
(108)x^2+2x-168=0
(109)x^2-6x-216=0
(110)x^2-6x-55=0
(111)x^2+18x+32=0
答案
(1)(3x+1)^2=7
解:
(3x+1)^2=7∴(3x+1)^2=7∴3x+1=±√7(注意不要丢解)∴x=(±√7-1)/3
(2)9x^2-24x+16=11
解:
9x^2-24x+16=11∴(3x-4)^2=11∴3x-4=±√11∴x=(±√11+4)/3∴原方程的解为x1=(√11+4)/3x2=(-√11+4)/3
(3)(x+3)(x-6)=-8
解:
(x+3)(x-6)=-8化简整理得x^2-3x-10=0(方程左边为二次三项式,右边为零)(x-5)(x+2)=0(方程左边分解因式)∴x-5=0或x+2=0(转化成两个一元一次方程)∴x1=5,x2=-2是原方程的解。
(4)2x^2+3x=0
解:
2x^2+3x=0x(2x+3)=0(用提公因式法将方程左边分解因式)∴x=0或2x+3=0(转化成两个一元一次方程)∴x1=0,x2=-3/2是原方程的解。
注意:
有些同学做这种题目时容易丢掉x=0这个解,应记住一元二次方程有两个解。
(5)6x^2+5x-50=0(选学)
解:
6x2+5x-50=0(2x-5)(3x+10)=0(十字相乘分解因式时要特别注意符号不要出错)∴2x-5=0或3x+10=0∴x1=5/2,x2=-10/3是原方程的解。
(6)x^2-4x+4=0(选学)
解:
x^2-4x+4=0(∵4可分解为2·2,∴此题可用因式分解法)(x-2)(x-2)=0∴x1=2,x2=2是原方程的解。
(7)(x-2)^2=4(2x+3)^2
解.(x-2)^2-4(2x+3)^2=0.[x-2+2(2x+3)][(x-2-2(2x+3)=0.
(5x+4)(-5x-8)=0.
x1=-4/5,x2=-8/5
(8)y^2+2√2y-4=0
解(y+√2)^2-2-4=0.
(y+√2)^2=6.
y+√2=√6.
y=-√2±√6.
y1=-√2+√6;
y2=-√2-√6.
(9)(x+1)^2-3(x+1)+2=0
解(x+1-1)(x+1-2)=0.
x(x-1)=0.
x1=0,
x2=1.
(10)x^2+2ax-3a^2=0(a为常数)
解(x+3a)(x-a)=0.
x1=-3a,
x2=a.
(11)2x^2+7x=4.
解:
方程可变形为2x^2+7x-4=0.
∵a=2,b=7,c=-4,b2-4ac=72-4×2×(-4)=81>0,
∴x=.∴x1=,x2=-4.
(12)x^2-1=2x
解:
方程可变形为x^2-2x-1=0.
∵a=1,b=-2,c=-1,b2-4ac=(-2)2-4×1×(-1)=16>0.
∴x=.∴x1=+2,x2=-2
(13)x^2+6x+5=0
解:
原方程可化为(x+5)(x+1)=0
x1=-5x2=-1
(14)x^2-4x+3=0
解:
原方程可化为(x-3)(x-1)=0
x1=3x2=1
(15)7x^2-4x-3=0
解原方程可化为(7x+3)(x-1)=0
x1=-3/7x2=1
(16)x^2-6x+9=0
解原方程可化为
(x-3)^2=0
x1=x2=3
(17)x²+8x+16=9
解:
(x+4)²=9
x+4=3或x+4=-3
x1=-1,x2=-7
(18)(x²-5)²=16
解:
x²-5=4或x²-5=-4
x²=9或x²=1
x1=3,x2=-3,x3=1,x4=-1
(19)x(x+2)=x(3-x)+1
解x²+2x=3x-x²+1
2x²-x-1=0
(2x+1)(x-1)=0
x1=-1/2x=1
(20)6x^2+x-2=0
解原方程可化为(3x+2)(2x-1)=0
(x+2/3)(x-1/2)=0
x1=-2/3x2=1/2
这是20道有过程的,还有一些没有过程,只有答案的。
1)x^2-9x+8=0答案:
x1=8x2=1
(2)x^2+6x-27=0答案:
x1=3x2=-9
(3)x^2-2x-80=0答案:
x1=-8x2=10
(4)x^2+10x-200=0答案:
x1=-20x2=10
(5)x^2-20x+96=0答案:
x1=12x2=8
(6)x^2+23x+76=0答案:
x1=-19x2=-4
(7)x^2-25x+154=0答案:
x1=14x2=11
(8)x^2-12x-108=0答案:
x1=-6x2=18
(9)x^2+4x-252=0答案:
x1=14x2=-18
(10)x^2-11x-102=0答案:
x1=17x2=-6
(11)x^2+15x-54=0答案:
x1=-18x2=3
(12)x^2+11x+18=0答案:
x1=-2x2=-9
(13)x^2-9x+20=0答案:
x1=4x2=5
(14)x^2+19x+90=0答案:
x1=-10x2=-9
(15)x^2-25x+156=0答案:
x1=13x2=12
(16)x^2-22x+57=0答案:
x1=3x2=19
(17)x^2-5x-176=0答案:
x1=16x2=-11
(18)x^2-26x+133=0答案:
x1=7x2=19
(19)x^2+10x-11=0答案:
x1=-11x2=1
(20)x^2-3x-304=0答案:
x1=-16x2=19
(21)x^2+13x-140=0答案:
x1=7x2=-20
(22)x^2+13x-48=0答案:
x1=3x2=-16
(23)x^2+5x-176=0答案:
x1=-16x2=11
(24)x^2+28x+171=0答案:
x1=-9x2=-19
(25)x^2+14x+45=0答案:
x1=-9x2=-5
(26)x^2-9x-136=0答案:
x1=-8x2=17
(27)x^2-15x-76=0答案:
x1=19x2=-4
(28)x^2+23x+126=0答案:
x1=-9x2=-14
(29)x^2+9x-70=0答案:
x1=-14x2=5
(30)x^2-1x-56=0答案:
x1=8x2=-7
(31)x^2+7x-60=0答案:
x1=5x2=-12
(32)x^2+10x-39=0答案:
x1=-13x2=3
(33)x^2+19x+34=0答案:
x1=-17x2=-2
(34)x^2-6x-160=0答案:
x1=16x2=-10
(35)x^2-6x-55=0答案:
x1=11x2=-5
(36)x^2-7x-144=0答案:
x1=-9x2=16
(37)x^2+20x+51=0答案:
x1=-3x2=-17
(38)x^2-9x+14=0答案:
x1=2x2=7
(39)x^2-29x+208=0答案:
x1=16x2=13
(40)x^2+19x-20=0答案:
x1=-20x2=1
(41)x^2-13x-48=0答案:
x1=16x2=-3
(42)x^2+10x+24=0答案:
x1=-6x2=-4
(43)x^2+28x+180=0答案:
x1=-10x2=-18
(44)x^2-8x-209=0答案:
x1=-11x2=19
(45)x^2+23x+90=0答案:
x1=-18x2=-5
(46)x^2+7x+6=0答案:
x1=-6x2=-1
(47)x^2+16x+28=0答案:
x1=-14x2=-2
(48)x^2+5x-50=0答案:
x1=-10x2=5
(49)x^2+13x-14=0答案:
x1=1x2=-14
(50)x^2-23x+102=0答案:
x1=17x2=6
(51)x^2+5x-176=0答案:
x1=-16x2=11
(52)x^2-8x-20=0答案:
x1=-2x2=10
(53)x^2-16x+39=0答案:
x1=3x2=13
(54)x^2+32x+240=0答案:
x1=-20x2=-12
(55)x^2+34x+288=0答案:
x1=-18x2=-16
(56)x^2+22x+105=0答案:
x1=-7x2=-15
(57)x^2+19x-20=0答案:
x1=-20x2=1
(58)x^2-7x+6=0答案:
x1=6x2=1
(59)x^2+4x-221=0答案:
x1=13x2=-17
(60)x^2+6x-91=0答案:
x1=-13x2=7
(61)x^2+8x+12=0答案:
x1=-2x2=-6
(62)x^2+7x-120=0答案:
x1=-15x2=8
(63)x^2-18x+17=0答案:
x1=17x2=1
(64)x^2+7x-170=0答案:
x1=-17x2=10
(65)x^2+6x+8=0答案:
x1=-4x2=-2
(66)x^2+13x+12=0答案:
x1=-1x2=-12
(67)x^2+24x+119=0答案:
x1=-7x2=-17
(68)x^2+11x-42=0答案:
x1=3x2=-14
(69)x^20x-289=0答案:
x1=17x2=-17
(70)x^2+13x+30=0答案:
x1=-3x2=-10
(71)x^2-24x+140=0答案:
x1=14x2=10
(72)x^2+4x-60=0答案:
x1=-10x2=6
(73)x^2+27x+170=0答案:
x1=-10x2=-17
(74)x^2+27x+152=0答案:
x1=-19x2=-8
(75)x^2-2x-99=0答案:
x1=11x2=-9
(76)x^2+12x+11=0答案:
x1=-11x2=-1
(77)x^2+17x+70=0答案:
x1=-10x2=-7
(78)x^2+20x+19=0答案:
x1=-19x2=-1
(79)x^2-2x-168=0答案:
x1=-12x2=14
(80)x^2-13x+30=0答案:
x1=3x2=10
(81)x^2-10x-119=0答案:
x1=17x2=-7
(82)x^2+16x-17=0答案:
x1=1x2=-17
(83)x^2-1x-20=0答案:
x1=5x2=-4
(84)x^2-2x-288=0答案:
x1=18x2=-16
(85)x^2-20x+64=0答案:
x1=16x2=4
(86)x^2+22x+105=0答案:
x1=-7x2=-15
(87)x^2+13x+12=0答案:
x1=-1x2=-12
(88)x^2-4x-285=0答案:
x1=19x2=-15
(89)x^2+26x+133=0答案:
x1=-19x2=-7
(90)x^2-17x+16=0答案:
x1=1x2=16
(91)x^2+3x-4=0答案:
x1=1x2=-4
(92)x^2-14x+48=0答案:
x1=6x2=8
(93)x^2-12x-133=0答案:
x1=19x2=-7
(94)x^2+5x+4=0答案:
x1=-1x2=-4
(95)x^2+6x-91=0答案:
x1=7x2=-13
(96)x^2+3x-4=0答案:
x1=-4x2=1
(97)x^2-13x+12=0答案:
x1=12x2=1
(98)x^2+7x-44=0答案:
x1=-11x2=4
(99)x^2-6x-7=0答案:
x1=-1x2=7
(100)x^2-9x-90=0答案:
x1=15x2=-6
(101)x^2+17x+72=0答案:
x1=-8x2=-9
(102)x^2+13x-14=0答案:
x1=-14x2=1
(103)x^2+9x-36=0答案:
x1=-12x2=3
(104)x^2-9x-90=0答案:
x1=-6x2=15
(105)x^2+14x+13=0答案:
x1=-1x2=-13
(106)x^2-16x+63=0答案:
x1=7x2=9
(107)x^2-15x+44=0答案:
x1=4x2=11
(108)x^2+2x-168=0答案:
x1=-14x2=12
(109)x^2-6x-216=0答案:
x1=-12x2=18
(110)x^2-6x-55=0答案:
x1=11x2=-5
(111)x^2+18x+32=0答案:
x1=-2x2=-16
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