Question

The sum of the roots of the equation. $x^2+\left|2x-3\right|-4=0$, is :

• A. $2$
• B. $-2$
• C. $\sqrt{2}$
• D. $\sqrt{-2}$

Answer 1

Answer: (C)

$x^2+|2x-3|-4=0$
Case- $1:x\ge \frac{3}{2}$
$\Rightarrow x^2+2x-3-4=0$
$\Rightarrow x=-1\pm 2\sqrt{2}$
$\Rightarrow x=-1+2\sqrt{2}$
Case - $2:x<\frac{3}{2}$
$\Rightarrow x^2-2x-1=0$
$\Rightarrow x=1\pm \sqrt{2}$
$\Rightarrow x=1-\sqrt{2}$
$\Rightarrow$ Sum $=\sqrt{2}$