For what value of k, (4-k) x²+ (2k+4) x+ (8k+1) =0, is a perfect square?

Answer 1

The polynomial (not the equation) is a perfect square if its roots are two equal real numbers.

The discriminant must be = 0.

(2k + 4)² - 4(4 - k)(8k + 1) = 0

As a Calculus student you should be able to solve fro k and answer?