I4.3 If $b-6, b-5, b-4$ are three roots of the equation $x^{4}+r x^{2}+s x+t=0$, find the value of $c=r+t$.
The three roots are 1,2 and 3 . Let the fourth root be $\alpha$.
$$
\begin{array}{l}
\alpha+1+2+3=0 \Rightarrow \alpha=-6 \\
r=-6 \times 1-6 \times 2-6 \times 3+1 \times 2+1 \times 3+2 \times 3=-25 \\
t=-6 \times 1 \times 2 \times 3=-36 \\
c=r+t=-25-36=-61
\end{array}
$$