Roots of equation left| {,begin{array}{*{20}{c}}0&x&{16}x&5&70&9&xend{array}

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3 and 4 .Determinants and Matrices

easy

The roots of the equation $\left| {\,\begin{array}{*{20}{c}}0&x&{16}\\x&5&7\\0&9&x\end{array}\,} \right| = 0$ are

A

$0,\,\,12,\,\,12$

B

$0, 12, -12$

C

$0, 12, 16$

D

$0, 9, 16$

Solution

(b) $\left| {\,\begin{array}{*{20}{c}}0&x&{16}\\x&5&7\\0&9&x\end{array}\,} \right|\, = \,0$

By expanding, we get $ – x({x^2} – 144) = 0$

$ \Rightarrow $ $x = 0$ or ${x^2} = 144$ $ \Rightarrow $ $x = \pm 12$

So, $x = 0$, $12,$ $ – 12$.

Standard 12

Mathematics

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