Question 11
Let
$$
f(x) = x^{4} - 6x^{3} + 26x^{2} - 46x + 65.
$$
Let the roots of $f(x)$ be $a_{k} + i b_{k}$ for $k = 1, 2, 3, 4$. Given that the $a_{k}, b_{k}$ are all integers, find $|b_{1}| + |b_{2}| + |b_{3}| + |b_{4}|$.
$$
f(x) = x^{4} - 6x^{3} + 26x^{2} - 46x + 65.
$$
Let the roots of $f(x)$ be $a_{k} + i b_{k}$ for $k = 1, 2, 3, 4$. Given that the $a_{k}, b_{k}$ are all integers, find $|b_{1}| + |b_{2}| + |b_{3}| + |b_{4}|$.