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  4. The sum of the roots of the equation. x2+|2x-3|-4=0, is :

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

JEE MainJEE Main 2014Complex Numbers and Quadratic Equations

Solution:

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