Question

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

Answer 1

6x² – 17ix – 12 = 0

Given 6x² – 17ix – 12 = 0

⇒ 6x² – 17ix – 12x1 = 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

x = \(\frac{3}{2}i,or\frac{4}{3}i\) 

Thus, the roots of the given equation are

\(\frac{3}{2}i,or\frac{4}{3}i\)