Question

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

Answer 1

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`.