Question 24
For certain real numbers $a,$ $b,$ and $c,$ the polynomial $$
g(x) = x^3 + ax^2 + x + 10
$$ has three distinct roots, and each root of $g(x)$ is also a root of the polynomial $$
\begin{aligned} f(x) &= x^4 + x^3 \\ &\quad {}+ bx^2 + 100x + c. \end{aligned}
$$ What is $f(1)?$
g(x) = x^3 + ax^2 + x + 10
$$ has three distinct roots, and each root of $g(x)$ is also a root of the polynomial $$
\begin{aligned} f(x) &= x^4 + x^3 \\ &\quad {}+ bx^2 + 100x + c. \end{aligned}
$$ What is $f(1)?$