Multiple choice

Product of real roots of the equation $\displaystyle x^{2}+\left | x \right |+9= 0$

  1. is always positive

  2. is always negative

  3. does not exist

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

The equation x^2 + |x| + 9 = 0 has no real roots because x^2 >= 0 and |x| >= 0, so x^2 + |x| + 9 is always >= 9.

AI explanation

For any real number x, the expression x^2 is always non-negative, the absolute value of x is non-negative, and the constant 9 is positive. The sum of three non-negative terms is always strictly greater than zero. Therefore, the equation can never equal zero for any real number. Because there are no real roots, their product does not exist.

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