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

Given: 9x² + 4 = 0

9x² + 4 × 1 = 0

We know, i² = –1 = 1 = –i²

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

So,

9x² + 4(–i²) = 0

9x² – 4i² = 0

(3x)² – (2i)² = 0

[By 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 = \( \dfrac{-2i}{3}\) or x =\( \dfrac{2i}{3}\)

The roots of the given equation are \( \dfrac{-2i}{3}, \dfrac{2i}{3}\)