Evaluate the following determinant : | cc x & -7 x & 5 x+1 | - Vidyadip

Question

Evaluate the following determinant : $\left|\begin{array}{cc}x & -7 \\ x & 5 x+1\end{array}\right|$

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Answer

(b) : We have, $\left|\begin{array}{cc}x & -7 \\ x & 5 x+1\end{array}\right|=x(5 x+1)+7(x)$
$
=5 x^2+x+7 x=5 x^2+8 x=x(5 x+8)
$

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