Question

For what real values of c is x^2 + 16x + c the square of a binomial? If you find more than one, then list your values separated by commas.

Answer 1

-10, 10

Explanation:

Comparing x^2 + ax + 25 to (x + b)^2 = x^2 + 2bx + b^2, we see that we must have b^2 = 25. This means that b = -5 or b = 5.

If b=5, we have (x+5)^2 = x^2 +10x + 25, and if b = -5, then we have (x-5)^2 = x^2 -10x + 25. Therefore, the two values of a for which x^2 + ax + 25 is the square of a binomial are -10, 10.