Question

Solve the quadratic equations by factorization method only:

4x² + 1 = 0

Answer 1

Given as 4x² + 1 = 0

As we know, i² = –1 ⇒ 1 = –i²

On substituting 1 = –i² in the above equation, we get

4x² – i² = 0

(2x)² – i² = 0

[On using the formula, a² – b² = (a + b) (a – b)]

(2x + i) (2x – i) = 0

2x + i = 0 or 2x – i = 0

2x = –i or 2x = i

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

∴ The roots of the given equation are i/2, -i/2