Let $\alpha$ and $\beta$ be the roots of the equation ${ \left| x \right| }^{ 2 }+\left| x \right| -6=0$, then the sum and product of both the roots are respectively-

Factoring the equation |x|^2 + |x| - 6 = 0 gives (|x| + 3)(|x| - 2) = 0, which means |x| must be either 2 or -3. Since the absolute value of x cannot be negative, |x| = 2, yielding the two roots x = 2 and x = -2. The sum of these roots is 2 + (-2) = 0, and their product is 2 * -2 = -4.

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