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The product and sum of the roots of the equation $\left|x^2\right|-5|x|-24=0$ are respectively
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Verified Answer
The correct answer is:
$-64,0$
(a) We have, $|x|^2-5|x|-24=0$
$\begin{aligned}
& \Rightarrow \quad(|x|-8)(|x|+3)=0 \\
& \Rightarrow \quad|x|-8 \text { or }|x|=-3 \text { is rejected. } \\
& \Rightarrow \quad|x|=8 \\
& \Rightarrow \quad x= \pm 8
\end{aligned}$
$\therefore \quad$ The roots of this equation. $a x=8$ and -8 .
Hence, product of roots $8 \times(-8)=-64$ and sum of roots $=+8-8=0$
$\begin{aligned}
& \Rightarrow \quad(|x|-8)(|x|+3)=0 \\
& \Rightarrow \quad|x|-8 \text { or }|x|=-3 \text { is rejected. } \\
& \Rightarrow \quad|x|=8 \\
& \Rightarrow \quad x= \pm 8
\end{aligned}$
$\therefore \quad$ The roots of this equation. $a x=8$ and -8 .
Hence, product of roots $8 \times(-8)=-64$ and sum of roots $=+8-8=0$
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