Solve the following quadratic equation by factorization:

$4\sqrt{3}x^2+5x-2\sqrt3=0$

Given:

Given quadratic equation is $4\sqrt{3}x^2+5x-2\sqrt3=0$.

To do:

We have to solve the given quadratic equation.

Solution:

$4\sqrt{3}x^2+5x-2\sqrt3=0$

To factorise $4\sqrt{3}x^2+5x-2\sqrt3=0$, we have to find two numbers $m$ and $n$ such that $m+n=5$ and $mn=4\sqrt{3}\times(-2\sqrt{3})=-8(\sqrt3)^2=-24$.

If $m=8$ and $n=-3$, $m+n=8-3=5$ and $mn=8(-3)=-24$.

$4\sqrt{3}x^2+8x-3x-2\sqrt3=0$

$\sqrt{3}x(4x-(\sqrt3)+2(4x-\sqrt3)=0$

$(\sqrt{3}x+2)(4x-\sqrt3)=0$

$\sqrt{3}x+2=0$ or $4x-\sqrt3=0$

$\sqrt{3}x=-2$ or $4x=\sqrt3$

$x=\frac{-2}{\sqrt3}$ or $x=\frac{\sqrt3}{4}$

$x=-\frac{2}{\sqrt3}$ or $x=\frac{\sqrt3}{4}$

The values of $x$ are $-\frac{2}{\sqrt3}$ and $\frac{\sqrt3}{4}$.

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Updated on: 10-Oct-2022

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