Q. A factor of $\mathrm{\Delta}(x) = \left| \begin{matrix} x^{3} + 1 & 2x^{4} + 3x^{2} & 3x^{5} + 4x \\ 2 & 5 & 7 \\ 3 & 14 & 19 \end{matrix} \right|$ is
A) $x$
B) $(x - 1)^{2}$
C) $(x + 1)^{2}$
D) None of these
Explanation
(b)
Since,$\ \mathrm{\Delta}(1) = 0\ and\ \mathrm{\Delta}^{'}(1) = 0\ so,\ (x - 1)^{2}\ is\ a\ factor\ of\ \mathrm{\Delta}(x)$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.