Q52 / 160 · AP EAMCET 2016 · Mathematics

The product and sum of the roots of the equation $\left|x^2\right|-5|x|-24=0$ are respectively

  • Correct answer
    A
    $-64,0$
  • B
    $-24, 5$
  • C
    $5, -24$
  • D
    $0, 72$

Solution

(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 $=+8-8=0$

Hence, the correct answer is option: 'A'.

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