Finding X: Determine When y=5x² is Greater Than Zero

Question

Given the function:

y=5x2 y=5x^2

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

Step-by-Step Solution

The given function is y=5x2 y = 5x^2 . This is a quadratic function where the coefficient of x2 x^2 is positive, making the parabolic shape open upwards.

The expression 5x2 5x^2 is always non-negative. For this function to be greater than zero, it should not be equal to zero. We find the expression equals zero when x=0 x = 0 .

When x0 x \neq 0 , 5x2 5x^2 is positive. Therefore, y=5x2>0 y = 5x^2 > 0 whenever x0 x \neq 0 . This applies to both positive and negative x x values, except for zero.

Thus, the correct answer is: x0 x \neq 0 .

Answer

x0 x\ne0