Question

Find the roots of quadratic equation √2x²+7x+5√2=0 , by factorisations method.

Answer 1

Given quadratic equation is √2x²+7x+5√2=0 .

We need to factorize this equation.

⇒ √2x² + 7x + 5√2 = 0

Now factorize middle term of the equation using middle term splitting method. [ 7 = 2 + 5 & 5 * 2 = 10 ]

⇒ √2x² + 2x + 5x + 5√2 = 0

⇒ √2x ( x + √2 ) + 5 ( x + √2 ) = 0

⇒ ( x + √2 ) ( √2x + 5 )

⇒ x = - √2 & x = - 5 /√2

So , Roots of the quadratic equation √2x²+7x+5√2=0 are - √2 & - 5 / √2

Answer 2

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{Value\:of\:x=-\sqrt{2}\:and\:\frac{-5}{\sqrt{2}}}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline \bold{Given :}} \\ \tt: \implies \sqrt{2}{x}^{2} + 7x + 5 \sqrt{2} = 0 \\ \\ \red{\underline \bold{To \: Find :}} \\ \tt: \implies Value \: of \: x = ?$

• According to given question :

$\bold{As \: we \: know \: that} \\ \tt: \implies \sqrt{2} {x}^{2} + 7x + 5 \sqrt{2} = 0 \\ \\ \tt: \implies \sqrt{2} {x}^{2} + 2x + 5x + 5 \sqrt{2} = 0 \\ \\ \tt: \implies \sqrt{2} x(x + \sqrt{2} ) + 5(x + \sqrt{2} ) = 0 \\ \\ \tt: \implies ( \sqrt{2}x + 5)(x + \sqrt{2} ) = 0 \\ \\ \green{\tt: \implies x = - \sqrt{2} \: and \: \frac{ - 5}{\sqrt{2} } } \\ \\ \bold{Alternate \: method : } \\ \tt: \implies x = \frac{ - b \pm \sqrt{ {b}^{2} - 4ac} }{2a} \\ \\ \tt: \implies x = \frac{ - 7 \pm \sqrt{ {7}^{2} - 4 \times \sqrt{2} \times 5 \sqrt{2} } }{2 \times \sqrt{2} } \\ \\ \tt: \implies x = \frac{ - 7 \pm \sqrt{49 -40 } }{2 \sqrt{2} } \\ \\ \tt: \implies x = \frac{ - 7 \pm 3}{2 \sqrt{2} } \\ \\ \green{\tt: \implies x = - \sqrt{2} \: and \: \frac{ - 5}{ \sqrt{2} } }$