Solve the quadratic equations by factorization method only 6x2 – 17ix – 12 = 0

6x² – 17ix – 12 = 0

Given: 6x² – 17ix – 12 = 0

6x² – 17ix – 12 × 1 = 0

We know, i² = –1 ⇒ 1 = –i²

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

6x² – 17ix – 12(–i²) = 0

6x² – 17ix + 12i² = 0

6x² – 9ix – 8ix + 12i² = 0

3x(2x – 3i) – 4i(2x – 3i) = 0

(2x – 3i) (3x – 4i) = 0

2x – 3i = 0 or 3x – 4i = 0

2x = 3i or 3x = 4i

x = \( \dfrac{3i}{2}\) or x = \( \dfrac{4i}{3}\)

The roots of the given equation are \( \dfrac{3i}{2}\), \( \dfrac{4i}{3}\)