Question

Given that 4x^2-32x-20+k is a perfect square find k​

Answer 1

• k = 20

Explanation:

Perfect square identity:

• (a + b)² = a² + 2ab + b²

Completing the square:

• 4x² - 32x - 20 + k =
• (2x)² - 2*2x*8 + 8² - 20 + k =
• (2x - 8)² - (20 - k)

In order the given to be a perfect square, we need:

• 20 - k = 0
• k = 20