设ax^2＋bx+c=0(a≠0)的两根分别为x1,x2
则有,ax1^2＋bx1+c=0 且 ax2^2＋bx2+c=0
两根之和为s1,两根的平房和为s2,两根的立方和为s3,
即s1=x1+x2 s2=x1^2+s2^2 s3=x1^3+x2^3
as3+bs2+cs1
= a(x1^3+x2^3)+b(x1^2+s2^2)+c(x1+x2)
= x1(ax1^2＋bx1+c)+ x2(ax2^2＋bx2+c)
= x1*0 +x2*0
= 0