Question

Find the roots given equations.
(I)${\sqrt{2x}}^2+7x+5\sqrt{2}=0$
(II) $2x^2-x+\frac{1}{8}=0$

Answer 1

We have,

PART (1):-

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

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

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

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

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

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

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

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

Hence, this is the answer.

We have,

PART (2):-

$2x^2-x+\frac{1}{8}=0$

$\Rightarrow 16x^2-8x+1=0$

$\Rightarrow 16x^2-(4+4)x+1=0$

$\Rightarrow 16x^2-4x-4x+1=0$

$\Rightarrow 4x(4x-1)-1(4x-1)=0$

$\Rightarrow (4x-1)(4x-1)=0$

$\Rightarrow 4x-1=0,4x-1=0$

$\Rightarrow 4x=1,4x=1$

$x=\frac{1}{4},\frac{1}{4}$

Hence, this is the answer.