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`