一元二次方程练习题含答案(解法20题)解析

1、经典解法20题(1)(3x+l)A2=7(2)9xA2-24x+16=ll(3)(x+3)(x-6)=-82xA2+3x=0(5)6x八2+5x-50=0(选学)(6)xA2-4x+4=0(选学)(x-2)A2=4(2x+3)A2(8)yA2+2V2y-4=0(9)(x+1)A2-3(x+l)+2=0(10)xA2+2ax-3aA2=0(a为常数)(ll)2xA2+7x=4.(12)xA2-l=2x(13)xA2+6x+5=0(14)xA2-4x+3=0(15)7xA2-4x-3=0(16)xA2-6x+9=0(17)x2+8x+16=9(18)(x2-5)2=16(19)x(x+2)=x(3

2、-x)+l(20)6xA2+x-2=0海量111题l)xA2-9x+8=0(2)xA2+6x-27=0(3)xA2-2x-80=0(4)xA2+10x-200=0x八2-20x+96=0(6)xA2+23x+76=0x八2-25X+154=0(8)xA2-12x-108=0(9)xA2+4x-252=0(10)xA2-llx-102=0(ll)x八2+15x-54=0(12)xA2+llx+18=0(13)xA2-9x+20=0(14)xA2+19x+90=0(15)xA2-25x+156=0(16)xA2-22x+57=0(17)xA2-5x-176=0(18)xA2-26x+133=0(1

3、9)xA2+10x-ll=0(20)xA2-3x-304=0(21)xA2+13x-140=0(22)xA2+13x-48=0(23)x八2+5X-176=0(24)x八2+28X+171=0(25)xA2+14x+45=0(26)x八2-9X-136=0(27)xA2-15x-76=0(28)xA2+23x+126=0(29)xA2+9x-70=0(30)x八2-1X-56二0(31)xA2+7x-60=0(32)xA2+10x-39=0(33)xA2+19x+34=0(34)xA2-6x-160=0(35)x八2-6X-55=0(36)x八2-7X-144=0(37)xA2+20x+51=

4、0(38)xA2-9x+14=0(39)xA2-29x+208=0(40)xA2+19x-20=0(41)xA2-13x-48=0(42)xA2+10x+24=0(43)x八2+28X+180=0(44)xA2-8x-209=0(45)xA2+23x+90=0(46)x八2+7x+6=0(47)xA2+16x+28=0(48)x八2+5x-50=0(49)xA2+13x-14=0(50)xA2-23x+102=0(51)xA2+5x-176=0(52)x八2-8X-20二0(53)xA2-16x+39=0(54)x八2+32x+240=0(55)x八2+34X+288=0(56)x八2+22X

5、+105=0(57)xA2+19x-20=0(58)xA2-7x+6=0(59)xA2+4x-221=0(60)xA2+6x-91=0(61)xA2+8x+12=0(62)xA2+7x-120=0(63)xA2-18x+17=0(64)xA2+7x-170=0(65)x八2+6x+8=0(66)xA2+13x+12=0(67)xA2+24x+119=0(68)xA2+llx-42=0(69)xA20x-289=0(70)xA2+13x+30=0(71)xA2-24x+140=0(72)xA2+4x-60=0(73)xA2+27x+170=0(74)x八2+27x+152=0(75)x八2-2X

6、-99=0(76)xA2+12x+ll=0(77)xA2+17x+70=0(78)xA2+20x+19=0(79)xA2-2x-168=0(80)x八2-13X+30=0(81)xA2-10x-119=0(82)xA2+16x-17=0(83)xA2-lx-20=0(84)x八2-2X-288=0(85)x八2-20x+64=0(86)xA2+22x+105=0(87)xA2+13x+12=0(88)xA2-4x-285=0(89)x八2+26X+133=0(90)xA2-17x+16=0(91)xA2+3x-4=0(92)x八2-14X+48=0(93)xA2-12x-133=0(94)x八

7、2+5x+4=0(95)x八2+6x-91=0(96)xA2+3x-4=0(97)xA2-13x+12=0(98)xA2+7x-44=0(99)xA2-6x-7=0(100)xA2-9x-90=0(101)xA2+17x+72=0(102)xA2+13x-14=0(103)xA2+9x-36=0(104)xA2-9x-90=0(105)xA2+14x+13=0(106)xA2-16x+63=0(107)xA2-15x+44=0(108)xA2+2x-168=0(109)xA2-6x-216=09(UO)x八2-6x-55=0(lll)xA2+18x+32=0答案(1)(3x+l)A2=7解：(

8、3x+l)A2=7/.(3x+l)A2=7:Jx+l=±V7(注意不要丢解)/.x=(±V7-l)/3(2)9x八2-24X+16=11解：9xA2-24x+16=ll/.(3x-4)A2=ll/.3x-4=±Vll/.x=(±Vll+4)/3.原方程的解为xl=(Vll+4)/3x2=(-Vll+4)/3(3)(x+3)(x-6)=-8解：(x+3)(x-6)=-8化简整理得xA2-3x-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).。-5=0或x+2=0(转化成两个一元一次方程).xl=5,x2=-2是原方程

9、的解。2x八2+3x=0解：2x八2+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)/.xl=O,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八2+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.xl=5/2,x2=-10/3是原方程的解。x八2-4X+4=0(选学)解：x八2-4X+4=0(v4可分解为2-2此题可用因式分解法)(x-2)(x-2)=0，x

10、l=2,x2=2是原方程的解。(x-2)八2=4(2x+3)A2解.(x-2)八2-4(2x+3)八2=0.x-2+2(2x+3)(x-2-2(2x+3)=0.(5x+4)(-5x-8)=0.xl=-4/5fx2=-8/5(8) yA2+2V2y-4=0解(y+V2)八224=0.(y+V2)A2=6.y+V2=V6.y=-V2±V6.yl=-V2+V6;y2=-V2-V6.(9) (x+1)A2-3(x+l)+2=0解(x+l-l)(x+l-2)=0.x(x-l)=0.xl=0,x2=l.(10)xA2+2ax-3aA2=0(a为常数)解(x+3a)(x-a)=0.xl=-3a,x

11、2=a.(ll)2x八2+7x=4.解：方程可变形为2xA2+7x-4=0.a=2,b=7,c=-4,b2-4ac=72-4x2x(-4)=81>0,/.x=./.xl=,x2=-4.(12)x0-1=2x解：方程可变形为xA2-2x-1=0.,/a=1,b=-2,c=-1,b2-4ac=(-2)2-4x1x(-1)=16>0./.x=./.xl=+2,x2=-2(13) xA2+6x+5=0解：原方程可化为(x+5)(x+l)=0xl=-5x2=-l(14) xA2-4x+3=0解：原方程可化为(x-3)(x-l)=0xl=3x2=l(15)7xA2-4x-3=0解原方程可化为(

12、7x+3)(x-l)=0xl=-3/7x2=l(16)xA2-6x+9=0解原方程可化为(x-3)A2=0xl=x2=3(17)x2+8x+16=9解：（x+4）2=9x+4=3或x+4=-3xl=-l,x2=-7(18)(x2-5)2=16解：x2-5=4或x2-5=-4x2=9或x2=lxl=3,x2=-3,x3=l,x4=-l(19)x(x+2)=x(3-x)+lWx2+2x=3x-x2+l2x2-x-l=0(2x+l)(x-l)=0xl=-l/2x=l(20)6x八2+x-2=0解原方程可化为(3x+2)(2x-1)=0(x+2/3)(x-l/2)=0xl=-2/3x2=l/2这是20

13、道有过程的，还有一些没有过程，只有答案的。l)xA2-9x+8=0答案:xl=8x2=lx八2+6x-27=0答案:xl=3x2=-9(3)xA2-2x-80=0答案：xl=-8x2=10(4)xA2+10x-200=0答案:xl=-20x2=10x八2-20x+96=0答案:xl=12x2=8(6)xA2+23x+76=0答案:xl=-19x2=-4(7)xA2-25x+154=0答案:xl=14x2=ll(8)xA2-12x-108=0答案:xl=-6x2=18(9)x八2+4x-252=0答案：xl=14x2=-18(10)xA2-llx-102=0答案:xl=17x2=-6(ll)x八

14、2+15x-54=0答案:xl=-18x2=3(12)xA2+llx+18=0答案：xl=-2x2=-9(13)xA2-9x+20=0答案：xl=4x2=5(14)xA2+19x+90=0答案：xl=-10x2=-9(15)xA2-25x+156=0答案：xl=13x2=12(16)x八2-22X+57=0答案:xl=3x2=19(17)xA2-5x-176=0答案：xl=16x2=-ll(18)xA2-26x+133=0答案:xl=7x2=19(19)xA2+10x-ll=0答案:xl=-llx2=l(20)x八2-3X-304二0答案：xl=-16x2=19(21)xA2+13x-140=

15、0答案:xl=7x2=-20(22)x八2+13X-48二0答案:xl=3x2=-16(23)xA2+5x-176=0答案:xl=-16x2=ll(24)xA2+28x+171=0答案:xl=-9x2=-19(25)xA2+14x+45=0答案:xl=-9x2=-5(26)x八2-9X-136二0答案：xl=-8x2=17(27)x八2-15X-76二0答案：xl=19x2=-4(28)x八2+23X+126=0答案:xl=-9x2=-14(29)xA2+9x-70=0答案：xl二-14x2=5(30)x八2-1X-56二0答案:xl=8x2=-7(31)xA2+7x-60=0答案：xl=5x

16、2=-12(32)x八2+10X-39二0答案:xl=-13x2=3(33)x八2+19x+34=0答案：xl=-17x2=-2(34)xA2-6x-160=0答案：xl=16x2=-10(35)x八2-6X-55二0答案:xl=llx2=-5(36)xA2-7x-144=0答案:xl=-9x2=16(37)x八2+20x+51=0答案：xl=-3x2=-17(38)xA2-9x+14=0答案：xl=2x2二7(39)xA2-29x+208=0答案：xl=16x2=13(40)xA2+19x-20=0答案:xl=-20x2=l(41)xA2-13x-48=0答案：xl=16x2=-3(42)x

17、A2+10x+24=0答案:xl=-6x2=-4(43)x八2+28x+180=0答案：xl=-10x2=-18(44)x八2-8X-209二0答案：xl=-llx2二19(45)xA2+23x+90=0答案:xl=-18x2=-5(46)x八2+7X+6=0答案：xl=-6x2=-l(47)x八2+16x+28=0答案：xl二-14x2=2(48)xA2+5x-50=0答案:xl=-10x2=5(49)xA2+13x-14=0答案:xl=lx2=-14(50)xA2-23x+102=0答案：xl=17x2=6(51)xA2+5x-176=0答案:xl=-16x2=ll(52)x八2-8X-2

18、0二0答案:xl=-2x2=10(53)xA2-16x+39=0答案:xl=3x2=13(54)x八2+32X+240二0答案：xl=-20x2=-12(55)xA2+34x+288=0答案:xl=-18x2=-16(56)x八2+22x+105=0答案：xl=-7x2=-15(57)xA2+19x-20=0答案:xl=-20x2=l(58)x八2-7x+6=0答案:xl=6x2=l(59)xA2+4x-221=0答案:xl=13x2=-17(60)xA2+6x-91=0答案：xl二-13x2=7(61)xA2+8x+12=0答案:xl=-2x2=-6(62)xA2+7x-120=0答案:xl

19、=-15x2=8(63)xA2-18x+17=0答案：xl=17x2=l(64)xA2+7x-170=0答案:xl=-17x2=10(65)x八2+6x+8=0答案：xl=-4x2=-2(66)xA2+13x+12=0答案：xl=-lx2=-12(67)x八2+24x+119=0答案：xl=-7x2=-17(68)xA2+llx-42=0答案:xl=3x2=-14(69)xA20x-289=0答案：xl=17x2=-17(70)xA2+13x+30=0答案:xl=-3x2=-10(71)xA2-24x+140=0答案:xl=14x2=10(72)x八2+4x-60=0答案：xl=-10x2=6

20、(73)x八2+27X+170二0答案:xl=-10x2=-17(74)x八2+27X+152=0答案：xl=-19x2=-8(75)x八2-2X-99二0答案:xl=llx2=-9(76)xA2+12x+ll=0答案:xl=-llx2=-l(77)xA2+17x+70=0答案:xl=-10x2=-7(78)xA2+20x+19=0答案:xl=-19x2=-l(79)xA2-2x-168=0答案:xl=-12x2=14(80)xA2-13x+30=0答案:xl=3x2=10(81)xA2-10x-119=0答案:xl=17x2=-7(82)xA2+16x-17=0答案:xl=lx2=-17(83)x八2-1X-20二0答案:xl=5x2=-4(84)x八2-2X-288二0答案：xl=18x2=-16(85)x八2-20x+64=0答案：xl=16x2=4(86)xA2+22x+105=0答案:xl=-7x2=-15(87)xA2+13x+12=0答案：xl=-lx2=-12(88)xA2-4