G5.1 If the roots of $x^{2}-2 x-P=0$ differ by 12 , find the value of $P$.
$\begin{array}{l}\alpha+\beta=2, \alpha \beta=-P \\ \alpha-\beta=12 \\ \Rightarrow(\alpha-\beta)^{2}=144 \\ \Rightarrow(\alpha+\beta)^{2}-4 \alpha \beta=144 \\ \Rightarrow 4+4 P=144 \\ \Rightarrow P=35\end{array}$