Show the following quadratic equation by factorization method: x^… - Vidyadip

Question

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

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Answer

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

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