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Question
Solving the following quadratic equation by factorization method:
\[6 x^2 - 17ix - 12 = 0\]
Solution
\[ 6 x^2 - 17ix - 12 = 0\]
\[ \Rightarrow 6 x^2 - 9ix - 8ix - 12 = 0\]
\[ \Rightarrow 3x\left( 2x - 3i \right) - 4i\left( 2x - 3i \right) = 0\]
\[ \Rightarrow \left( 2x - 3i \right)\left( 3x - 4i \right) = 0\]
\[ \Rightarrow \left( 2x - 3i \right) = 0 or \left( 3x - 4i \right) = 0\]
\[ \Rightarrow x = \frac{3}{2}i, \frac{4}{3}i\]
\[\text { So, the roots of the given quadratic equation are } \frac{3}{2}i \text { and } \frac{4}{3}i . \]
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