Show the following quadratic equation by factorization method: 3x… - Vidyadip

Question

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

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Answer

$\sqrt{3}\text{x}^2-\sqrt{2 }\text{x}+2\sqrt{3}=0$
We will apply discriminant rule,
$\text{x}=\frac{-\text{b}\pm\sqrt{\text{D}}}{2\text{a}}\ ...(\text{A})$
Where $D = b^2 - 4ac$
$=(-\sqrt{2})^2-4.\sqrt{3}.3\sqrt{3}$
$= 2 - 36$
$= -34$
From $(A)$
$\text{x}=\frac{-(-2)\pm\sqrt{-34}}{2.\sqrt{3}}$
$=\frac{\sqrt{2}\pm\sqrt{34}\text{ i}}{2\sqrt{3}}$
$\therefore\text{x}=\frac{\sqrt{2}\pm\sqrt{34}\text{ i}}{2\sqrt{3}}$

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