Solve the following quadratic equations by factorization method:

Question

Solve the following quadratic equations by factorization method: 6x 2 – 17ix – 12 = 0

Philoid · Accepted Answer

6x² – 17ix – 12 = 0

Given 6x² – 17ix – 12 = 0

⇒ 6x² – 17ix – 12 × 1 = 0

We have 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

Thus, the roots of the given equation are and.