Finding X in the Quadratic Inequality: Where y = -x² < 0

To solve this problem, we'll analyze the quadratic function $y = -x^2$.

• Step 1: Determine when $y = -x^2$ is less than zero.
  The function value is zero at $x = 0$ and less than zero for any other $x$. Since $-x^2$ will be negative for all non-zero $x$, this means $f(x) < 0$ for all $x \ne 0$.
• Step 2: Interpretation of results.
  The graph of $y = -x^2$ opens downward and only touches the x-axis at $x = 0$. This means, except at the point where $x = 0$, the function outputs negative values.
• Step 3: Comparison with given choices.
  We want $f(x) < 0$. Since this holds for all $x \ne 0$, we will select the answer $x \ne 0$.

Therefore, the solution to the problem is $x \ne 0$.