Question

If there are two values of ' $a$ ' which makes determinant
$\Delta=\begin{vmatrix}1 & -2 & 5 \\ 2 & a & -1 \\ 0 & 4 & 2 a\end{vmatrix}=86$
Then the sum of these numbers is

• A. $-4$
• B. 4
• C. 9
• D. 5

Answer 1

Answer: (A)

$\Delta=1\left(2 a^{2}+4\right)+2(4 a-0)+5(8)=86$
$2 a^{2}+8 a+44-86=0$
$2 a^{2}+8 a-42=0$
$a^{2}+4 a-21=0$
Sum of numbers $=-4\left(\therefore-\frac{ b }{ a }=\alpha+\beta\right)$