Question:
Write the number of real roots of the equation $x^{2}+3|x|+2=0$.
Solution:
The given quadric equation is $x^{2}+3|x|+2=0$
$x^{2}+3|x|+2=0$
Here, $a=1, b=\pm 3$ and, $c=2$
As we know that $D=b^{2}-4 a c$
Putting the value of $a=1, b=\pm 3$ and, $c=2$
$=(\pm 3)^{2}-4 \times 1 \times 2$
$=9-8$
$=1$
Since, $D \geq 0$
Therefore, roots of the given equation are real and distinct.
$\therefore$ The number of real roots of the given equation is 4 .
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