Determine the X Values: Inequality in Quadratics with y = -3/5x²

Given the function $y=-\frac{3}{5}x^2$

Determine for which values of x the following holds:

$f(x) < 0$

To solve the problem of finding when $f(x) = -\frac{3}{5}x^2 < 0$, we utilize properties of quadratic functions:

• The given function is $y = -\frac{3}{5}x^2$, where the coefficient of $x^2$ is $-\frac{3}{5}$.
• The negative coefficient indicates the parabola opens downwards.
• For any quadratic function of the form $y = ax^2$ where $a < 0$, the function is negative for all $x$ except at $x = 0$, where it equals zero.

Therefore, the function $f(x) = -\frac{3}{5}x^2$ is negative for all $x$ except $x = 0$.

Thus, the set of $x$ satisfying the condition $f(x) < 0$ is $x \neq 0$.

Hence, the solution is $x \ne 0$.