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

Question

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

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Answer

$\text{x}^2−(2+\text{i})\text{x}+\sqrt{2\text{i}}=0$
$\text{x}^2-\sqrt{2}\text{x}-\text{ix}+\sqrt{2}\text{i}=0$
$\text{x}(\text{x}-\sqrt{2})-\text{i}(\text{x}-\sqrt{2})=0$
$(\text{x}-\text{i})(\text{x}-\sqrt{2})=0$
$\text{x}=\text{i},\sqrt{2}$

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