Question

There are two values of a which makes determinant, ∆ = `|(1, -2, 5),(2, "a", -1),(0, 4, 2"a")|` = 86, then sum of these number is ______.

Options

• 4

• 5

• – 4

• 9

Answer 1

There are two values of a which makes determinant, ∆ = `|(1, -2, 5),(2, "a", -1),(0, 4, 2"a")|` = 86, then sum of these number is – 4.

Explanation:

We have, ∆ = `|(1, -2, 5),(2, "a", -1),(0, 4, 2"a")|` = 86

⇒ 1(2a² + 4) –2(–4a – 2) + 0 = 86  .....[Expanding along C₁]

⇒ a² + 4a – 21 = 0

⇒ (a + 7)(a – 3) = 0

⇒ a = –7 and 3

∴ Required sum = –7 + 3 = –4