Question

Find all real values of $s$ such that $x^2 + sx + 144 - 63$ is the square of a binomial.

Answer 1

First simplify: 144 − 63 = 81, so the polynomial is x^2 + s x + 81. If this equals (x + t)^2 = x^2 + 2t x + t^2 for some real t, then t^2 = 81 so t = ±9 and s = 2t. Hence s = 18 or s = −18.