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Find the roots of the following quadratic equations by factorisation: root 2 x ^2 + 7x + 5 root 2 = 0

Q1.    Find the roots of the following quadratic equations by factorisation:

                (iii)    \sqrt2x^2 + 7x + 5\sqrt2 = 0

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Given the quadratic equation: \sqrt2x^2 + 7x + 5\sqrt2 = 0

Factorisation gives, \sqrt2x^2 + 5x+2x + 5\sqrt2 = 0

\Rightarrow x(\sqrt2 x +5) +\sqrt2 (\sqrt 2 x +5)= 0

\Rightarrow (\sqrt2 x +5)(x+\sqrt{2}) = 0

\Rightarrow x=\frac{-5}{\sqrt 2 }\ or\ -\sqrt 2

Hence, the roots of the given quadratic equation are

 \frac{-5}{\sqrt 2 }\ and\ -\sqrt 2.

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