F x2 + mx + m is a perfect-square trinomial, which equation must be true?

Question

asked Mar 2, 2019 69.7k views

1 Answer

Jpmorris · Answer 1 · 2019-03-06T00:50:10+0000

For
x^2+mx+m to be a perfect square trinomial, we would need to have

(x+k)^2=x^2+2kx+k^2=x^2+mx+m

which means
m,k must satisfy

$\begin{cases}2k=m\\k^2=m\end{cases}\implies2k=k^2$

So

$2k=k^2\implies k^2-2k=k(k-2)=0\implies k=0\text{ or }k=2$

If
k=0 , then
m=0 , but then
x^2+mx+m is a monomial. If
k=2 , then
m=4 .