(1)方程:x2-x-12=0的根是:x1=-3,x2=4,则 x1+ x2=1,x1.x2=12 ; (2) 方程:2x2-7x+3=0的根是:x1 =½,x2=3,则 x1+ x2=7/2 x1.x2= ;(3) x2-3x+1=0的根是:x1=____,x2=_____,则 x1+ x2=____,x1.x2=_________ ;根据以上(1)(2)
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![(1)方程:x2-x-12=0的根是:x1=-3,x2=4,则 x1+ x2=1,x1.x2=12 ; (2) 方程:2x2-7x+3=0的根是:x1 =½,x2=3,则 x1+ x2=7/2 x1.x2= ;(3) x2-3x+1=0的根是:x1=____,x2=_____,则 x1+ x2=____,x1.x2=_________ ;根据以上(1)(2)](/uploads/image/z/5176609-25-9.jpg?t=%EF%BC%881%EF%BC%89%E6%96%B9%E7%A8%8B%EF%BC%9Ax2-x-12%3D0%E7%9A%84%E6%A0%B9%E6%98%AF%EF%BC%9Ax1%3D-3%2Cx2%3D4%2C%E5%88%99+x1%2B+x2%3D1%2Cx1.x2%3D12+%3B+%282%29+%E6%96%B9%E7%A8%8B%EF%BC%9A2x2-7x%2B3%3D0%E7%9A%84%E6%A0%B9%E6%98%AF%EF%BC%9Ax1+%3D%26frac12%3B%2Cx2%3D3%2C%E5%88%99+x1%2B+x2%3D7%2F2+x1.x2%3D+%3B%283%29+x2-3x%2B1%3D0%E7%9A%84%E6%A0%B9%E6%98%AF%EF%BC%9Ax1%3D____%2Cx2%3D_____%2C%E5%88%99+x1%2B+x2%3D____%2Cx1.x2%3D_________+%3B%E6%A0%B9%E6%8D%AE%E4%BB%A5%E4%B8%8A%EF%BC%881%EF%BC%89%EF%BC%882%EF%BC%89)
(1)方程:x2-x-12=0的根是:x1=-3,x2=4,则 x1+ x2=1,x1.x2=12 ; (2) 方程:2x2-7x+3=0的根是:x1 =½,x2=3,则 x1+ x2=7/2 x1.x2= ;(3) x2-3x+1=0的根是:x1=____,x2=_____,则 x1+ x2=____,x1.x2=_________ ;根据以上(1)(2)
(1)方程:x2-x-12=0的根是:x1=-3,x2=4,则 x1+ x2=1,x1.x2=12 ;
(2) 方程:2x2-7x+3=0的根是:x1 =½,x2=3,则 x1+ x2=7/2 x1.x2= ;
(3) x2-3x+1=0的根是:x1=____,x2=_____,则 x1+ x2=____,x1.x2=_________ ;
根据以上(1)(2)(3)你能否猜出:
如果关于x的一元二次方程mx2+nx+p=0,(m≠0且m,n,p为常数)的两根为x1x2,那么x1+ x2,
x1,x2与系数m,n,p有什么关系?请写出来你的猜想并说明理由.
(1)方程:x2-x-12=0的根是:x1=-3,x2=4,则 x1+ x2=1,x1.x2=12 ; (2) 方程:2x2-7x+3=0的根是:x1 =½,x2=3,则 x1+ x2=7/2 x1.x2= ;(3) x2-3x+1=0的根是:x1=____,x2=_____,则 x1+ x2=____,x1.x2=_________ ;根据以上(1)(2)
(3)x1=(3+根号5)/2 x2=(3-根号5)/2
x1+x2=3 x1x2=1
猜想:x1+x2=-n/m x1x2=p/m
证明:
x1=[-n+根号(n^2-4mp)]/2m x2=[-n-根号(n^2-4mp)]/2m
x1+x2=[-n+根号(n^2-4mp)-n-根号(n^2-4mp)]/2m=-2n/2m=-n/m
x1x2=[-n+根号(n^2-4mp)][-n-根号(n^2-4mp)]/(4m)^2=n^2-(n^2-16mp)/16m^2=16mp/16m^2=p/m
*注:n^2即n的平方
.·、°o·_________________________________i'M__aSamIya·Noay__
x1+x2=-n/m
x1.x2=p/m
(3):x1=3
x2=1