Multiple choice

The number of real roots for the equation x2 + 9|x| + 20 = 0 is:

  1. Zero

  2. One

  3. Two

  4. Three
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A Correct answer
Explanation

For x^2 + 9|x| + 20 = 0, notice that x^2 is equivalent to |x|^2. The equation becomes |x|^2 + 9|x| + 20 = 0, which factors to (|x| + 4)(|x| + 5) = 0. Since |x| must be non-negative, |x| = -4 or |x| = -5 have no real solutions.

AI explanation

The equation x2 + 9|x| + 20 = 0 has no real solutions because both terms are strictly positive for any real value of x. For any non-negative x, x2 and 9|x| are non-negative, and their sum with 20 must be at least 20, which is never zero. Thus, the number of real roots is zero.

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