Multiple choice

The real roots of the equation $x^2 + 5|x| + 4 = 0$ are

  1. $(-1, -4)$
  2. $(1, 4)$
  3. $(-4, 4)$

  4. No real root
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

For x^2 + 5|x| + 4 = 0, let y = |x|. Then y^2 + 5y + 4 = 0. (y+1)(y+4) = 0. y = -1 or y = -4. Since |x| cannot be negative, there are no real roots.

AI explanation

For any real number x, the value of |x| is always non-negative, meaning |x| >= 0. Consequently, both terms 5|x| and 4 are non-negative, making their sum x^2 + 5|x| + 4 always greater than or equal to 4. Since the left side can never equal zero, there are no real roots.

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