Question

Use the method of completing the square to transform the quadratic equation into the equation form (x – p)^2 = q.

12 - 8x^2 + x^4 = 0

A) (x2 - 4)2 = -4

B) (x2 - 4)2 = 4

C) (x2 - 2)2 = -4

D) (x2 - 2)2 = 4

Answer 1

x⁴ - 8x² = 0
x⁴ - 8x² + 16 = 0 + 16
x⁴ - 4x² - 4x² + 16 = 16
x²(x²) - x²(4) - 4(x²) + 4(4) = 16
x²(x² - 4) - 4(x² - 4) = 16
(x² - 4)(x² - 4) = 16
(x² - 4)² = 16

The answer is B.