Q. The roots of the equation $x^{4} - 8x^{2} - 9 = 0$ are
A) $\pm \ 1,\ \pm \ i$
B) $\pm \ 3,\ \pm \ i$
C) $\pm \ 2,\ \pm \ i$
D) None of these
Explanation
(b)
$\because\ x^{4} - 8x^{2} - 9 = 0$
$\Rightarrow x^{4} - 9x^{2} + x^{2} - 9 = 0$
$\Rightarrow x^{2}\left( x^{2} - 9 \right) + 1\left( x^{2} - 9 \right) = 0$
$\Rightarrow \left( x^{2} + 1 \right)\left( x^{2} - 9 \right) = 0$
$\Rightarrow x = \pm i,\ \pm 3$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.