Multiple choice

The quadratic equation $x^2+15|x|+14=0$ has

  1. Only positive solutions

  2. Only negative solutions

  3. No solution

  4. Both positive and negative solution
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Since |x| is always non-negative, x^2 + 15|x| + 14 = 0 involves only non-negative terms (x^2 >= 0, 15|x| >= 0, 14 > 0). The sum of these terms cannot be zero.

AI explanation

Because the square of any real number is always positive, x squared is greater than or equal to zero, and the absolute value of x is also greater than or equal to zero. This means the sum x squared plus 15 times the absolute value of x plus 14 will always be at least 14, which is strictly greater than zero for all real values of x. Since the left side can never equal zero, there is no real solution to the equation.

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