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Determinants — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsDeterminants1 Mark
MCQ
There are two value of a which makes the determinant $\triangle=\begin{vmatrix}1&-2&5\\2&\text{a}&-1\\0&4&2\text{a}\end{vmatrix}$ equal to $86$. The sum of these two values is:
  • A
    $4$
  • B
    $5$
  • ✓
    $-4$
  • D
    $9$
✓

Answer

Correct option: C.
$-4$
$\triangle=\begin{vmatrix}1&-2&5\\2&\text{a}&-1\\0&4&2\text{a}\end{vmatrix}=86$
$\Rightarrow 1(2a^2 + 4) - 2(-4a - 20) = 86$
$\Rightarrow 2a^2 + 4 + 8a + 40 = 86$
$\Rightarrow 2a^2 + 8a - 42 = 0$
$\Rightarrow a^2 + 4a - 21 = 0$
$\Rightarrow a^2+ 7a - 3a - 21 = 0$
$\Rightarrow a(a + 7) - 3(a + 7) = 0$
$\Rightarrow a = -7, 3$
Sum of the two values of $a = -7 + 3 = -4$
Hence, the correct option is $(c)$

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