If $\begin{vmatrix}1&-2&5\\2&a&-1\\0&4&2a\end{vmatrix}=86$, then product of all values of $a$ is:
Answer & explanation
Correct answer: option 2
The correct answer is Option (3) → 10
$\begin{vmatrix}1 & -2 & 5 \\[4pt] 2 & a & -1 \\[4pt] 0 & 4 & 2a\end{vmatrix}=86$
$=1\cdot\begin{vmatrix}a & -1 \\[4pt] 4 & 2a\end{vmatrix}-(-2)\cdot\begin{vmatrix}2 & -1 \\[4pt] 0 & 2a\end{vmatrix}+5\cdot\begin{vmatrix}2 & a \\[4pt] 0 & 4\end{vmatrix}$
$=1(2a^{2}+4)+2(4a)+5(8)=2a^{2}+8a+44$
$2a^{2}+8a+44=86\Rightarrow 2a^{2}+8a-42=0\Rightarrow a^{2}+4a-21=0$
$(a+7)(a-3)=0\Rightarrow a=-7,\,3$
Product of all values $= -21$