# Write the sum of real roots of the equation x2 + |x| − 6 = 0.

Question:

Write the sum of real roots of the equation $x^{2}+|x|-6=0$.

Solution:

The given quadric equation is $x^{2}+|x|-6=0$

Here, $a=1, b=\pm 1$ and, $c=-6$

As we know that $D=b^{2}-4 a c$

Putting the value of $a=1, b=\pm 1$ and, $c=-6$

$=(\pm 1)^{2}-4 \times 1 \times-6$

$=1+24$

$=25$

Since, $D \geq 0$

Therefore, root of the given equation are real and distinct.

Thus, sum of the roots be $=0$