Question

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

• A. $-4$
• B. 4
• C. 9
• D. 5

Answer 1

Answer: (A)

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