How do you find the values of k that will make #x^2 + kx +36# a perfect square?

1 Answer
Jul 9, 2016

Consider the equation #0 = x^2 + 4x + 4#. We can solve this by factoring as a perfect square trinomial, so #0 = (x+ 2)^2-> x = -2 and -2#. Hence, there will be two identical solutions.

The discriminant of the quadratic equation (#b^2 - 4ac#) can be used to determine the number and the type of solutions. Since a quadratic equations roots are in fact its x intercepts, and a perfect square trinomial will have #2# equal, or #1# distinct solution, the vertex lies on the x axis. We can set the discriminant to 0 and solve:

#k^2 - (4 xx 1 xx 36) = 0#

#k^2 - 144 = 0#

#(k + 12)(k - 12) = 0#

#k = +-12#

So, k can either be #12# or #-12#.

Hopefully this helps!