The function below describes the curve that forms a graph of the cross-section for a parabolic dish.
\large f\left(x\right)=3x^2-17x+10
What is the sum of the zeros for the function?
To find the zeros of the function, we need to set it equal to zero and solve for x:
\begin{align*}
3x^2 - 17x + 10 &= 0 \\
(3x - 2)(x - 5) &= 0 \\
x &= \frac23 \text{ or } x = 5
\end{align*}
Therefore, the sum of the zeros is:
\begin{align*}
\frac23 + 5 &= \frac{15}{3} + \frac{2}{3} \\
&= \frac{17}{3}
\end{align*}
So the answer is $\boxed{\frac{17}{3}}$.