If there are two values of ' a ' which makes determinant Δ=|1 -2 5 2 a -1 0 4 2 a|=86 Then the sum of these numbers is

Question

If there are two values of ' a ' which makes determinant Δ=|1 -2 5 2 a -1 0 4 2 a|=86 Then the sum of these numbers is (A) -4 (B) 4 (C) 9 (D) 5

Tardigrade Admin · Accepted Answer

Δ=1(2 a2+4)+2(4 a-0)+5(8)=86 2 a2+8 a+44-86=0 2 a2+8 a-42=0 a2+4 a-21=0 Sum of numbers =-4(∴-( b / a )=α+β)

Q. If there are two values of ' $a$ ' which makes determinant
$Δ = ∣ ∣ 120 - 2 a 4 5 - 1 2 a ∣ ∣ = 86$
Then the sum of these numbers is