Multiple choice

Find the number of roots of the equation: $\displaystyle \left | x \right |^{2}-7\left | x \right |+12=0 $

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

  4. cannot determine
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let u = |x|. u^2 - 7u + 12 = 0 => (u-3)(u-4) = 0. So |x| = 3 or |x| = 4. This gives x = 3, -3, 4, -4. Total 4 roots.

AI explanation

Factoring the quadratic in |x| gives (|x| - 3)(|x| - 4) = 0, yielding |x| = 3 and |x| = 4. Solving |x| = 3 gives the two roots x = 3 and x = -3. Similarly, solving |x| = 4 gives x = 4 and x = -4. Combining these yields four real roots: 3, -3, 4, and -4.

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