Question

find the root of the following quadratic equation by factorization method √2x²+7x +5√2​

Answer 1

Given equation

$\sqrt2} x^{2} +7x+5\sqrt{2}=0$

Solving, we get,

$\sqrt{2} x^{2} +7x+5\sqrt{2} =0$

$\implies \sqrt{2} x^{2} +2x+5x+5\sqrt{2} = 0$

$\implies \sqrt{2} x(x+\sqrt{2})+5(x+\sqrt{2}) = 0$

$\implies (\sqrt{2} x+5)(x+\sqrt{2}) = 0$

Now,

$\sqrt{2} x+5=0$

$\implies \boxed{\boxed{\bold{ x = \dfrac{-5}{\sqrt{2} } }}}}$

$x+\sqrt{2} =0$

$\implies \boxed{\boxed{\bold{ x = -\sqrt{2} }}}}}}$

                                                       

Answer 2

$\rule{200}3$

$\bigstar\Huge{\green{\underline{\textsf{Question}}}}$

find the root of the following quadratic equation by factorization method $\sf \sqrt{2}x^2 + 7x + 5 \sqrt {2}$

$\rule{200}3$

$\bigstar\Huge{\red{\underline{\textsf{Answer}}}}$

$\longrightarrow$ $\sf \sqrt{2}x^2 + 7x + 5 \sqrt {2} = 0$

$\longrightarrow$ $\sf \sqrt{2}x^2 + 5x + 2x + 5 \sqrt {2} = 0$

$\longrightarrow$ $\sf x {(\sqrt{2}x+5)} + \sqrt {2} ( \sqrt {2}x + 5) = 0$

$\longrightarrow$ $\sf x {(\sqrt{2}x+5)}(x + \sqrt{2}) = 0$

$\longrightarrow$ $\sf x + \sqrt 2 = 0$

$\orange\longrightarrow$ $\boxed{ \sf\orange{ x = - \sqrt{2}}}$

$\longrightarrow$ $\sf \sqrt {2}x + 5 = 0$

$\purple\longrightarrow$ $\boxed{\sf\purple {x = {\frac{-5}{\sqrt{2}}}}}$

$\rule{200}3$

❤️$\mathcal{BE \: BRAINLY}$❤️

$\rule{200}3$