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Question
Solve the following quadratic equation:
\[i x^2 - x + 12i = 0\]
Solution
\[i x^2 - x + 12i = 0\]
\[ \Rightarrow i\left( x^2 + ix + 12 \right) = 0\]
\[ \Rightarrow x^2 + ix + 12 = 0\]
\[ \Rightarrow x^2 + 4ix - 3ix + 12 = 0\]
\[ \Rightarrow x\left( x + 4i \right) - 3i\left( x + 4i \right) = 0\]
\[ \Rightarrow \left( x + 4i \right)\left( x - 3i \right) = 0\]
\[ \Rightarrow \left( x + 4i \right) = 0 \text { or} \left( x - 3i \right) = 0\]
\[ \Rightarrow x = - 4i , 3i\]
\[\text { So, the roots of the given quadratic equation are - 4i and } 3i .\]
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