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3 and 4 . determinant and metrices — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths3 and 4 . determinant and metrices1 Mark
MCQ
The determinant $\left| {\,\begin{array}{*{20}{c}}{4 + {x^2}}&{ - 6}&{ - 2}\\{ - 6}&{9 + {x^2}}&3\\{ - 2}&3&{1 + {x^2}}\end{array}\,} \right|$ is not divisible by
  • A
    $x$
  • B
    ${x^3}$
  • C
    $14 + {x^2}$
  • ✓
    ${x^5}$
✓

Answer

Correct option: D.
${x^5}$
d
(d) $\left| {\,\begin{array}{*{20}{c}}{4 + {x^2}}&{ - 6}&{ - 2}\\{ - 6}&{9 + {x^2}}&3\\{ - 2}&3&{1 + {x^2}}\end{array}} \right| = {x^4}(14 + {x^2})$ $ = x.{x^3}(14 + {x^2})$

Hence, the determinant is divisible by $x$,${x^3}$ and $(14 + {x^2})$,

but not divisible by ${x^5}$.

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