Question

Product of real roots of the equation $x^2+\left|x\right|+9=0$

• A. is always positive
• B. is always negative
• C. does not exist
• D. none of these

Answer 1

The correct option is C does not exist

$x^2+|x|+9$
$=|x{|}^2+|x|+9$
$=0$
Hence,
$(|x|+\frac{1}{2}{)}^2-\frac{1}{4}+9=0$
$(|x|+\frac{1}{2}{)}^2+\frac{35}{4}$
Hence, we would always get imaginary roots.
Thus, product of real roots does not exist.