Question

Solve the quadratic equations by factorization method only:

4x² – 12x + 25 = 0

Answer 1

Given as 4x² – 12x + 25 = 0

4x² – 12x + 9 + 16 = 0

(2x)² – 2(2x)(3) + 3² + 16 = 0

(2x – 3)² + 16 = 0 [Since, (a + b)² = a² + 2ab + b²]

(2x – 3)² + 16 × 1 = 0

As we know, i² = –1 ⇒ 1 = –i²

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

(2x – 3)² + 16(–i²) = 0

(2x – 3)² – 16i² = 0

(2x – 3)² – (4i)² = 0

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

(2x – 3 + 4i) (2x – 3 – 4i) = 0

2x – 3 + 4i = 0 or 2x – 3 – 4i = 0

2x = 3 – 4i or 2x = 3 + 4i

x = 3/2 – 2i or x = 3/2 + 2i

∴ The roots of the given equation are 3/2 + 2i, 3/2 – 2i