Show the following quadratic equation: x^2-(32+2i)x+62 i=0 - Vidyadip

Question

Show the following quadratic equation:
$\text{x}^2-(3\sqrt{2}+2\text{i})\text{x}+6\sqrt{2}\text{ i}=0$

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Answer

$\text{x}^2-(3\sqrt{2}+2\text{i})\text{x}+6\sqrt{2}\text{ i}=0$
$\Rightarrow\text{x}^2-3\sqrt{2}\text{x}-2\text{ix}+\sqrt{2}\text{i}=0$
$\Rightarrow\text{x}(\text{x}-3\sqrt{2})-2\text{i}(\text{x}-3\sqrt{2})=0$
$\Rightarrow(\text{x}-2\text{i})(\text{x}-3\sqrt{2})=0$
$\Rightarrow\text{x}=2\text{i}\ \text{or }3\sqrt{2}$

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