Question 23
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 $$
\begin{aligned} &f(x)=x^4+x^3+bx^2 \\ &\quad {}+100x+c. \end{aligned}
$$ 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+bx^2 \\ &\quad {}+100x+c. \end{aligned}
$$ What is $f(1)?$