Find the roots of the following quadratic equations by the factorisation method:
$ 3 \sqrt{2} x^{2}-5 x-\sqrt{2}=0 $

Given:

Given quadratic equation is \( 3 \sqrt{2} x^{2}-5 x-\sqrt{2}=0 \).

To do:

We have to find the roots of the given quadratic equation.

Solution:

\( 3 \sqrt{2} x^{2}-5 x-\sqrt{2}=0 \)

$3 \sqrt{2} x^{2}-(6 x-x)-\sqrt{2}=0$

$3 \sqrt{2} x^{2}-6 x+x-\sqrt{2}=0$

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

$3 \sqrt{2} x(x-\sqrt{2})+1(x-\sqrt{2})=0$

$(x-\sqrt{2})(3 \sqrt{2} x+1)=0$

$x-\sqrt{2}=0$ or $3 \sqrt{2} x+1=0$

$x =\sqrt{2}$ or $x=-\frac{1}{3 \sqrt{2}}$

$x =\sqrt{2}$ or $x=-\frac{\sqrt{2}}{3\sqrt{2}\times \sqrt2}$

$x =\sqrt{2}$ or $x=-\frac{\sqrt{2}}{6}$

Hence, the roots of the given quadratic equation are $\sqrt{2}, -\frac{\sqrt{2}}{6}$. 

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Updated on: 10-Oct-2022

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