Question

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

Answer 1

Hey There!

Since you have given your age as 18, I am going to assume you know about Quadratic Equations.

Here, we are given that $x^2+mx+m$ is a perfect square trinomial.

This means that, this polynomial has two real and equal zeros.

In order to find the zeros, we usually write as:
$x^2+mx+m=0$

For real and equal roots, the Discriminant must be zero. Only then the polynomial can be a perfect square trinomial.

So,
$D = b^2-4ac = 0 \\ \\ \implies m^2 - 4(1)(m) = 0 \\ \\ \implies \boxed{m^2-4m=0}$

This equation must be true, if the polynomial has to be a perfet square trinomial.


We can also solve it further:

$m^2-4m=0 \\ \\ \implies m(m-4) = 0 \\ \\ \implies m=0 \, \, \, OR \, \, \, m=4$

Thus, the two quadratic polynomials become:
$1) \, m=0 \\ \\ \implies \boxed{x^2} \\ \\ \\ 2) \, m=4 \\ \\ \implies \boxed{x^2+4x+4}$

Hope it helps
Purva
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