x^2+11x +c

Question

Find the value of c that makes each trinomial a perfect square. Then write the trinomial as a perfect square.

Answer 1

A trinomial that was a perfect square (with a leading coefficient of 1) is formed by multiplying (x + a)(x + a) to get x² + 2ax + a². Looking at the linear coefficient of our original equation, 2a = 11, so a = 11/2. We then square this to get a² = (11/2)² = 121/4

So our new trinomial is x² + 11x + 121/4