Question

If $a$ is a constant such that $4x^2 - 12x + a$ is the square of a binomial, then what is $a$?

Answer 1

Set (2x + b)^2 = 4x^2 + 4bx + b^2. Matching coefficients with 4x^2 - 12x + a gives 4b = -12 ⇒ b = -3 and a = b^2 = 9.

So a = 9.