Multiple choice

The sum of real roots of the equation $\displaystyle x^{2}+|x|-6=0$ is

  1. $4$
  2. $0$
  3. $-1$

  4. none of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The equation is x^2 + |x| - 6 = 0. If x >= 0, x^2 + x - 6 = 0 -> (x+3)(x-2) = 0, so x = 2. If x < 0, x^2 - x - 6 = 0 -> (x-3)(x+2) = 0, so x = -2. The sum of roots 2 + (-2) = 0.

AI explanation

For x greater than or equal to 0, the equation becomes x squared plus x minus 6 equals 0. Factoring gives (x plus 3)(x minus 2) equals 0, and the only non-negative root is 2. For x less than 0, the equation becomes x squared minus x minus 6 equals 0. Factoring gives (x minus 3)(x plus 2) equals 0, and the only negative root is negative 2. The sum of the real roots 2 and negative 2 is 0.

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