Question

若x^4-6x^3+13x^2+kx+4是一个完全平方式,求常数k的值

Answer 1

k＝－12

设

x^4-6x^3+13x^2+kx+4

=(x^2-mx+n)^2

=x^4-2mx^3+(m^2+2n)x^2-2mnx+n^2,

对比系数知,

2m=6,

n^2=4,

m^2+2n=13,

-2mn=k,

解得,

m＝3,

n＝2,

k＝－12