a(x-x1)(x-x2)=ax^2-a(x1+x2)x+ax1x2.(1)
x1+x2=-b/a.(2)
x1x2=c/a.(3)
(2),(3)代入(1)得
a(x-x1)(x-x2)=ax^2-a(x1+x2)x+ax1x2
=ax^2-a*(-b/a)x+a*c/a
=ax^2+bx+c
a(x-x1)(x-x2)=ax^2-a(x1+x2)x+ax1x2.(1)
x1+x2=-b/a.(2)
x1x2=c/a.(3)
(2),(3)代入(1)得
a(x-x1)(x-x2)=ax^2-a(x1+x2)x+ax1x2
=ax^2-a*(-b/a)x+a*c/a
=ax^2+bx+c