Solve the following quadratic equation by factorization:

$3\sqrt{5}x^2+25x-10\sqrt5=0$

Given:

Given quadratic equation is $3\sqrt{5}x^2+25x-10\sqrt5=0$.

To do:

We have to solve the given quadratic equation.

Solution:

$3\sqrt{5}x^2+25x-10\sqrt5=0$

To factorise $3\sqrt{5}x^2+25x-10\sqrt5=0$, we have to find two numbers $m$ and $n$ such that $m+n=25$ and $mn=3\sqrt{5}\times(-10\sqrt{5})=-30(\sqrt5)^2=-150$.

If $m=30$ and $n=-5$, $m+n=30-5=25$ and $mn=30(-5)=3\sqrt{5}\times(-10\sqrt{5})=-150$.

$3\sqrt{5}x^2+30x-5x-10\sqrt5=0$

$3\sqrt{5}x(x+2\sqrt5)-5(x+2\sqrt5)=0$

$(3\sqrt{5}x-5)(x+2\sqrt5)=0$

$3\sqrt{5}x-5=0$ or $x+2\sqrt5=0$

$3\sqrt{5}x=5$ or $x=-2\sqrt5$

$x=\frac{5}{3\sqrt5}$ or $x=-2\sqrt5$

$x=\frac{\sqrt5}{3}$ or $x=-2\sqrt5$

The values of $x$ are $x=\frac{\sqrt5}{3}$ or $x=-2\sqrt5$.

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Updated on: 10-Oct-2022

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