Multiple choice

The roots of the equation ${ \left| x \right| }^{ 2 }+\left| x \right| -6=0$ are

  1. only one real no.

  2. real and sum = 1

  3. real and sum = 0

  4. real and product = 0
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let u = |x|. The equation is u^2 + u - 6 = 0, which factors to (u+3)(u-2) = 0. Since u = |x| >= 0, u = 2. Thus |x| = 2, so x = 2 or x = -2. The roots are 2 and -2, and their sum is 0.

AI explanation

Treating the absolute value of x as a variable, we can factor the quadratic equation as (absolute value of x + 3)(absolute value of x - 2) = 0. This gives the absolute value of x as -3 or 2, but since absolute value cannot be negative, the absolute value of x must be 2. This yields two real roots, x = 2 and x = -2, whose sum is 2 + (-2) = 0. The result is real and sum = 0.

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