There are two values of a which makes the determinant \[∆ = \begin{vmatrix}1 & - 2 & 5 \\ 2 & a & - 1 \\ 0 & 4 & 2a\end{vmatrix}\] equal to 86. The sum of these two values is

There Are Two Values of a Which Makes the Determinant δ = ∣ ∣ ∣ ∣ 1 − 2 5 2 a − 1 0 4 2 a ∣ ∣ ∣ ∣ Equal to 86. the Sum of These Two Values is (A) 4 (B) 5 (C) −4 (D) 9 - Mathematics

Question

There are two values of a which makes the determinant $∆ = | \begin{matrix} 1 & - 2 & 5 \\ 2 & a & - 1 \\ 0 & 4 & 2 a \end{matrix} |$ equal to 86. The sum of these two values is

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MCQ

Solution

$∆ = | \begin{matrix} 1 & - 2 & 5 \\ 2 & a & - 1 \\ 0 & 4 & 2 a \end{matrix} | = 86$
$\Rightarrow 1 (2 a^{2} + 4) - 2 (- 4 a - 20) = 86$
$\Rightarrow 2 a^{2} + 4 + 8 a + 40 = 86$
$\Rightarrow 2 a^{2} + 8 a - 42 = 0$
$\Rightarrow a^{2} + 4 a - 21 = 0$
$\Rightarrow a^{2} + 7 a - 3 a - 21 = 0$
$\Rightarrow a (a + 7) - 3 (a + 7) = 0$
$\Rightarrow (a + 7) (a - 3) = 0$
$\Rightarrow a = - 7, 3$
$Sum of the two values of a = - 7 + 3 = - 4 .$

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Applications of Determinants and Matrices

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Q 31 Q 30 Q 32

Chapter 6: Determinants - Exercise 6.7 [Page 96]

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Chapter 6 Determinants
Exercise 6.7 | Q 31 | Page 96

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There Are Two Values of a Which Makes the Determinant δ = ∣ ∣ ∣ ∣ 1 − 2 5 2 a − 1 0 4 2 a ∣ ∣ ∣ ∣ Equal to 86. the Sum of These Two Values is (A) 4 (B) 5 (C) −4 (D) 9 - Mathematics

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There Are Two Values of a Which Makes the Determinant δ = ∣ ∣ ∣ ∣ 1 − 2 5 2 a − 1 0 4 2 a ∣ ∣ ∣ ∣ Equal to 86. the Sum of These Two Values is (A) 4 (B) 5 (C) −4 (D) 9 - Mathematics

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