由韦达定理x1+x2=-(k-1)x1x2=kx1²+x2²=6即(x1+x2)²-2x1x2=6k²-2k+1-2k=6x²-4x-5=0(k-5)(k+1)=0k=5,k=-1有实根,判别式大于等于0(k-1)²-4k>0k=5时不成立所以k=-1