Question

Solve the following quadratic equation:

\[x^2 - \left( 3\sqrt{2} + 2i \right) x + 6\sqrt{2i} = 0\]

Answer 1

\[ x^2 - \left( 3\sqrt{2} + 2i \right) x + 6\sqrt{2}i = 0\]

\[ \Rightarrow x^2 - 3\sqrt{2} x - 2i x + 6\sqrt{2}i = 0\]

\[ \Rightarrow x\left( x - 3\sqrt{2} \right) - 2i\left( x - 3\sqrt{2} \right) = 0\]

\[ \Rightarrow \left( x - 3\sqrt{2} \right)\left( x - 2i \right) = 0\]

\[ \Rightarrow \left( x - 3\sqrt{2} \right) = 0 \text { or } \left( x - 2i \right) = 0\]

\[ \Rightarrow x = 3\sqrt{2}, 2i\]

\[\text { So, the roots of the given quadratic equation are 3 }\sqrt{2} \text { and } 2i . \]