Consider the polynomial function $f(x) = 3x^3 - 5x^2 + ax + b$. If the function has a root at $x = 2$, what is the value of $a + b$ if it is given that $f(2) = 0$?
To find the unknowns $a$ and $b$, substitute $x = 2$ into the polynomial and solve the resulting equation:
$f(2) = 3(2)^3 - 5(2)^2 + 2a + b = 0$.