Roots of equation left| {,begin{array}{*{20}{c}}x&0&84&1&32&0&xend{array},}

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3 and 4 .Determinants and Matrices

easy

The roots of the equation $\left| {\,\begin{array}{*{20}{c}}x&0&8\\4&1&3\\2&0&x\end{array}\,} \right| = 0$ are equal to

A

$( - 4,\,4)$

B

$(2,\, - 4)$

C

$(2,\,4)$

D

$(2,\,8)$

Solution

(a) We have $\left| {\,\begin{array}{*{20}{c}}x&0&8\\4&1&3\\2&0&x\end{array}\,} \right|\, = 0$

$\therefore $ $\Delta = x(x – 0) – 0(4x – 6) + 8(0 – 2)$

or ${x^2} – 16 = 0$ $ \Rightarrow $ $x = 4,\, – 4$.

Standard 12

Mathematics

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(JEE MAIN-2023)