Question

Find the zeros of the function f(x) = -5x^2 + 4x - 1 by completing the square.

Answer 1

x = 2/5 + 1/5 i and x = 2/5 - 1/5 i

Explanation:

f(x) = -5x^2 + 4x - 1

-5x² + 4x - 1 = 0

Divide both sides by -5.

x² - (4/5)x + 1/5 = 0

x² - (4/5)x + 4/25 = -1/5 + 4/25

(x - 2/5)² = -5/25 + 4/25

(x - 2/5)² = -1/25

x - 2/5 = ±√(-1/25)

x = 2/5 ± i/5

x = 2/5 + 1/5 i and x = 2/5 - 1/5 i