Identifying Values of X for Which 5x² < 0: A Quadratic Inquiry

Given the function:

$y=5x^2$

Determine for which values of x $f\left(x\right) < 0$ holds

To solve this problem, consider the nature of the quadratic function $y = 5x^2$. The function has a leading coefficient of 5, which is positive, indicating that the parabola opens upwards.

A parabola opening upwards, such as this one, has its minimum value at the vertex. For the function $y = 5x^2$, the minimum value occurs at $x = 0$, where $y = 5 \cdot 0^2 = 0$. Since $y = 5x^2$ is a non-negative quadratic for all real $x$, the function $f(x) = 5x^2 \geq 0$ for all $x$.

This means that there are no values of $x$ for which $f(x) < 0$ holds. The function is only zero when $x = 0$ and positive otherwise for any non-zero $x$.

Conclusively, there are no values of $x$ where $f(x) < 0$. Therefore, the solution is that no $x$ satisfies $f(x) < 0$.

Hence, the answer is that there are