For the equation ${ \left| x \right| }^{ 2 }+\left| x \right| -6=0$
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There are four roots
- The sum of the root is $-1$
- The product of the roots is $-4$
- The product of the roots is $-6$
Reveal answer
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C
Correct answer
Explanation
Let u = |x|. The equation becomes u^2 + u - 6 = 0, which factors to (u + 3)(u - 2) = 0. Since |x| cannot be negative, |x| = 2, meaning x = 2 or x = -2. The product of these roots is 2 * (-2) = -4.
AI explanation
Let y equal the absolute value of x, transforming the equation into y squared plus y minus 6 equals 0, which factors as the quantity y plus 3 times the quantity y minus 2 equals 0. Since y is an absolute value, it must be non-negative, so y equals 2. This gives the absolute value of x equals 2, meaning the roots are 2 and negative 2. The product of these roots is 2 times negative 2, which equals negative 4.