Find the roots of the following quadratic equ | vedclass

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(A) Given equation is $3 \sqrt{2} x^{2}-5 x-\sqrt{2}=0$.To factorise,we split the middle term $-5x$ into $-6x + x$ such that their product is $(3 \sqr

Vedclass · Accepted Answer

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

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(A) Given equation is $3 \sqrt{2} x^{2}-5 x-\sqrt{2}=0$.To factorise,we split the middle term $-5x$ into $-6x + x$ such that their product is $(3 \sqrt{2}) 	imes (-\sqrt{2}) = -6$.$3 \sqrt{2} x^{2}-6 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$Setting each factor to zero:$x-\sqrt{2}=0 \Rightarrow x=\sqrt{2}$$3 \sqrt{2} x+1=0 \Rightarrow x=-\frac{1}{3 \sqrt{2}}$.Rationalizing the denominator: $x = -\frac{1 	imes \sqrt{2}}{3 \sqrt{2} 	imes \sqrt{2}} = -\frac{\sqrt{2}}{3 	imes 2} = -\frac{\sqrt{2}}{6}$.Thus,the roots are $-\frac{\sqrt{2}}{6}$ and $\sqrt{2}$.

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

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