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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 $\sqrt{2}, -\frac{\sqrt{2}}{6}$.