Multiple choice

Product of the roots of the equation $x^{2}+3|x|-28=0$ is

  1. $0$
  2. $-16$
  3. $16$
  4. $-28$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

By substituting y = |x| (where y must be non-negative), the equation becomes y^2 + 3y - 28 = 0, which factors into (y + 7)(y - 4) = 0. Since y cannot be negative, we have y = 4, which gives the real roots x = 4 and x = -4. The product of these roots is 4 * (-4) = -16.

AI explanation

To solve the equation x^2 + 3|x| - 28 = 0, consider the two cases for the absolute value based on the sign of x. For x positive, the equation becomes x^2 + 3x - 28 = 0, which factors into (x + 7)(x - 4) = 0, yielding the positive root x = 4. For x negative, the equation becomes x^2 - 3x - 28 = 0, which factors into (x - 7)(x + 4) = 0, yielding the negative root x = -4. The product of these two valid roots, 4 and -4, is -16.

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