若方程(x-1)(x2+8x-3)=0的三根分别为x1,x2,x3,则x1x2+x2x3+x3x1的值是(  ) A.5 B.-5 C.11 D.-11

问题描述:

若方程(x-1)(x2+8x-3)=0的三根分别为x1,x2,x3,则x1x2+x2x3+x3x1的值是(  )
A. 5
B. -5
C. 11
D. -11

∵方程(x-1)(x2+8x-3)=0的三根分别为x1,x2,x3
∴x1=1,x3+x2=-8,x3•x2=-3,
则x1x2+x2x3+x3x1=x1(x2+x3)+x2x3=-3-8=-11.
故选D.