For the equation |{x^2}| + |x| - 6 = 0, the r | vedclass

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Question

(c) When $x < 0$, $|x| = - x$

Equation is ${x^2} - x - 6 = 0 \Rightarrow x = - 2,\,3$

$\;x < 0,\;	herefore \;x =  - 2$is the solutio

Vedclass · Accepted Answer

Real with sum zero

Vedclass · Answer

(c) When $x < 0$, $|x| = - x$ Equation is ${x^2} - x - 6 = 0 \Rightarrow x = - 2,\,3$ $\;x < 0,\; herefore \;x = - 2$is the solution. When $x \ge 0$,$|x| = x$ $ herefore $ Equation is${x^2} + x - 6 = 0 \Rightarrow x = 2, - 3$ $x \ge 0$, $x = 2$ is the solution. Hence $x = 2$, $ - 2$ are the solutions and their sum is zero. Aliter : $|{x^2}| + |x| - 6 = 0$ ==> $(|x| + 3)(|x| - 2) = 0$ ==> $|x| = - 3$, which is not possible and $|x| = 2$ ==> $x = \pm 2$.

For the equation $|{x^2}| + |x| - 6 = 0$, the roots are

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