Question

determine the zeros in y = -5x^3 + 16x

Answer 1

To determine the zeros of the function \( y = -5x^3 + 16x \), we need to solve the equation:

\[
-5x^3 + 16x = 0
\]

First, we can factor out a common term from the equation:

\[
x(-5x^2 + 16) = 0
\]

This gives us one zero immediately:

\[
x = 0
\]

Next, we need to solve the quadratic equation:

\[
-5x^2 + 16 = 0
\]

We can rearrange this to:

\[
5x^2 = 16
\]

Dividing both sides by 5 gives:

\[
x^2 = \frac{16}{5}
\]

Taking the square root of both sides:

\[
x = \pm \sqrt{\frac{16}{5}} = \pm \frac{4}{\sqrt{5}} = \pm \frac{4\sqrt{5}}{5}
\]

Thus, the zeros of the function \( y = -5x^3 + 16x \) are:

\[
x = 0, \quad x = \frac{4\sqrt{5}}{5}, \quad x = -\frac{4\sqrt{5}}{5}
\]