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DETERMINANTS — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsDETERMINANTS1 Mark
Question
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:
  1. 4
  2. 5
  3. -4
  4. 9
✓

Answer

  1. -4

Solution:

$\triangle=\begin{vmatrix}1&-2&5\\2&\text{a}&-1\\0&4&2\text{a}\end{vmatrix}=86$

⇒ 1(2a2 + 4) - 2(-4a - 20) = 86

⇒ 2a2 + 4 + 8a + 40 = 86

⇒ 2a2 + 8a - 42 = 0

⇒ a2 + 4a - 21 = 0

⇒ a2 + 7a - 3a - 21 = 0

⇒ a(a + 7) - 3(a + 7) = 0

⇒ a = -7, 3

Sum of the two values of a = -7 + 3 = -4

Hence, the correct option is (c)

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