Question

Determine the value(s) of k for which the expression is a perfect square trinomial. x^2+kx+36

Answer 1

If the quadratic is a perfect square, then there has to be a way to write the quadratic as $(x - r)^2$, where $r$ is a root of the equation. Expanding it out, we see that

$(x - r)^2 = x^2 - 2rx + r^2$

Now let's compare this form to the one that we were given. Since $r^2$ matches up with $36$, $r$ has to equal either $6$ or $-6$. So, since $kx$ in the original equation matches up with $-2rx$ in the equation we found, $k = -2r$ and

$\bf k = -12$ or $\bf 12$