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Determinants — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsDeterminants1 Mark
Question
Find value of $x$, if $\left| {\begin{array}{*{20}{c}} 2&4 \\ 5&1 \end{array}} \right| = \left| {\begin{array}{*{20}{c}} {2x}&4 \\ 6&x \end{array}} \right|$
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Answer

$ (2-20)=\left(2 x^2-24\right) $
$ -18=2 x^2-24 $
$ -2 x^2=-24+18 $
$ -2 x^2=-6 $
$ 2 x^2=6 $
$ x^2=3 $
$ x= \pm \sqrt{3}$

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