Question

Solve 4x^4=1-3x^2 for all complex roots​

Answer 1

4x⁴ = 1 - 3x²

4x⁴ + 3x² - 1 = 0

Factor the left side:

(4x² - 1) (x² + 1) = 0

((2x)² - 1²) (x² - i ²) = 0

(2x + 1) (2x - 1) (x - i ) (x + i ) = 0

Then

2x + 1 = 0 or 2x - 1 = 0 or x - i = 0 or x + i = 0

Solve for x :

x = -1/2 or x = 1/2 or x = i or x = -i