There are two numbers x making the value of the determinant |1 -2 5 2 x -1 0 4 2 x| equal to 86 . The sum of these two numbers, is

Question

There are two numbers x making the value of the determinant |1 -2 5 2 x -1 0 4 2 x| equal to 86 . The sum of these two numbers, is (A) -4 (B) 5 (C) -3 (D) 9

Tardigrade Admin · Accepted Answer

D=(2 x2+4)-2(-4 x-20) =2 x2+8 x+44=86 =2 x2+8 x-42=0 ⇒ x2+4 x-21=0 ⇒ α+β=-4

Q. There are two numbers $x$ making the value of the determinant $∣ ∣ 120 - 2 x 4 5 - 1 2 x ∣ ∣$ equal to 86 . The sum of these two numbers, is

-4

5

-3

9

$D = (2 x^{2} + 4) - 2 (- 4 x - 20)$
$= 2 x^{2} + 8 x + 44 = 86$
$= 2 x^{2} + 8 x - 42 = 0$
$\Rightarrow x^{2} + 4 x - 21 = 0$
$\Rightarrow α + β = - 4$

Q. There are two numbers x making the value of the determinant ∣∣​120​−2x4​5−12x​∣∣​ equal to 86 . The sum of these two numbers, is

-4

5

-3

9

D=(2x2+4)−2(−4x−20) =2x2+8x+44=86 =2x2+8x−42=0 ⇒x2+4x−21=0 ⇒α+β=−4

Q. There are two numbers $x$ making the value of the determinant $∣ ∣ 120 - 2 x 4 5 - 1 2 x ∣ ∣$ equal to 86 . The sum of these two numbers, is

$D = (2 x^{2} + 4) - 2 (- 4 x - 20)$
$= 2 x^{2} + 8 x + 44 = 86$
$= 2 x^{2} + 8 x - 42 = 0$
$\Rightarrow x^{2} + 4 x - 21 = 0$
$\Rightarrow α + β = - 4$