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(A) To find the roots of the quadratic equation $\sqrt{2} x^{2}+7 x+5 \sqrt{2}=0$ by factorisation:$1$. Split the middle term $7x$ into two parts such

Vedclass · Accepted Answer

$x = -\frac{5}{\sqrt{2}}, x = -\sqrt{2}$

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(A) To find the roots of the quadratic equation $\sqrt{2} x^{2}+7 x+5 \sqrt{2}=0$ by factorisation:$1$. Split the middle term $7x$ into two parts such that their sum is $7x$ and their product is $(\sqrt{2} x^{2}) 	imes (5 \sqrt{2}) = 10x^{2}$.$2$. The two parts are $5x$ and $2x$ because $5x + 2x = 7x$ and $5x 	imes 2x = 10x^{2}$.$3$. Rewrite the equation: $\sqrt{2} x^{2} + 2x + 5x + 5 \sqrt{2} = 0$.$4$. Factor by grouping: $\sqrt{2} x(x + \sqrt{2}) + 5(x + \sqrt{2}) = 0$.$5$. Take out the common factor $(x + \sqrt{2})$: $(x + \sqrt{2})(\sqrt{2} x + 5) = 0$.$6$. Set each factor to zero:- $x + \sqrt{2} = 0 \implies x = -\sqrt{2}$- $\sqrt{2} x + 5 = 0 \implies \sqrt{2} x = -5 \implies x = -\frac{5}{\sqrt{2}}$Thus,the roots are $x = -\sqrt{2}$ and $x = -\frac{5}{\sqrt{2}}$.

Find the roots of the following quadratic equation by factorisation:
$\sqrt{2} x^{2}+7 x+5 \sqrt{2}=0$

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Find the roots of the following quadratic equation by factorisation:$\sqrt{2} x^{2}+7 x+5 \sqrt{2}=0$