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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
Solution
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
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