Factorize:$x^2 - \sqrt{3}x - 6$

Given :

$x^2 - \sqrt{3}x - 6$

To do :

We have to factorize the given expression.

Solution :

$x^2 - \sqrt{3}x - 6=x^{2}-2 \sqrt{3} x+ \sqrt{3} x-6$                  [Since $-2 \sqrt{3} x+\sqrt{3} x=- \sqrt{3} x$ and $-2 \sqrt{3} x\times\sqrt{3} x=-6\times x^2$]

$=x(x-2\sqrt{3})+ \sqrt{3}(x-2 \sqrt{3})$

$=(x-2 \sqrt{3})(x+\sqrt{3})$

Hence, $x^2 - \sqrt{3}x - 6=(x-2 \sqrt{3})(x+\sqrt{3})$.

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Updated on: 10-Oct-2022

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