Question

Let $P(x)=\begin{vmatrix} x^2-13 & 4 & 2 \\ 3 & x^2-13 & 7 \\ 6 & 5 & x^2-13 \end{vmatrix}$
If $x=-2$ is a zero of $P(x)$, then sum of the remaining five zeros is

• A. -2
• B. 0
• C. 2
• D. 3

Answer 1

Answer: (C)

As coefficient of $x^5$ in $P(x)$ is 0 , sum of six zeros of $P(x)$ is 0
. $\Rightarrow$ sum of the remaining five zeros $+(-2)=0$
$\Rightarrow$ sum of the remaining five zeros $=2$.