Question

Find the product of the roots of the equation $\left|x^2\right|-4\left|x\right|-21=0$

• A. -21
• B. 21
• C. -49
• D. -4

Answer 1

The correct option is C

-49

Product of the roots is $\frac{c}{a}$ if the given equation is a quadratic in x only. The given equation is a quadratic in $\left|x\right|$. So the product of the roots may not be $\frac{c}{a}$. So we will find the roots and multiply them to get the product of the roots.

$\left|x^2\right|-4\left|x\right|-21=0$

Let y = $\left|x\right|$
$\Rightarrow y^2-4y-21=0$
(y-7)(y+3) = 0
y=7 or y=-3
But y can't be -3 $\left(\right|x\left|\right)\ge 0$
So $\left|x\right|)$ = 7
Or
x=7 or -7
$\Rightarrow$ 7,-7 are the roots
Product of roots = 7 X -7
=-49