Solve the quadratic equations by factorization method only: 9x2 + 4

1.	Solve the quadratic equations by factorization method only: 9x2 + 4 = 0
Answer» Given as 9x² + 4 = 0 9x² + 4 × 1 = 0 As we know, i² = –1 ⇒ 1 = –i² On substituting 1 = –i² in the above equation, we get Therefore, 9x² + 4(–i²) = 0 9x² – 4i² = 0 (3x)² – (2i)² = 0 [On using the formula, a² – b² = (a + b) (a – b)] (3x + 2i) (3x – 2i) = 0 3x + 2i = 0 or 3x – 2i = 0 3x = –2i or 3x = 2i x = -2i/3 or x = 2i/3 Thus, the roots of the given equation are 2i/3, -2i/3

Solve the quadratic equations by factorization method only: 9x2 + 4 = 0

Answer»

Given as 9x² + 4 = 0

9x² + 4 × 1 = 0

As we know, i² = –1 ⇒ 1 = –i²

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

Therefore,
9x² + 4(–i²) = 0

9x² – 4i² = 0

(3x)² – (2i)² = 0

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

(3x + 2i) (3x – 2i) = 0

3x + 2i = 0 or 3x – 2i = 0

3x = –2i or 3x = 2i

x = -2i/3 or x = 2i/3

Thus, the roots of the given equation are 2i/3, -2i/3