设这两个实根为x1,x2,则有
x1 x2=-b/(2a)
x1x2=c/a
因此
S1=x1^3 x2^3
=(x1 x2)(x1^2-x1x2 x2^2)
=(x1 x2)(x1^2 2x1x2-3x1x2 x2^2)
=(x1 x2)[(x1 x2)^2-3x1x2]
=[-b/(2a)]{[-b/(2a)]^2-3c/a}
S2=x1^2 x2^2
=x1^2 x2^2 2x1x2-2x1x2
=(x1 x2)^2-2x1x2
=[-b/(2a)]^2-2c/a
S3=x1 x2
=-b/(2a)
那么
aS1 bS2 cS3
…………
把S1,S2,S3用a、b、c代表的式子代入上面的式子,就可以了.