I5.1 If the sum of roots of $5 x^{2}+a x-2=0$ is twice the product of roots, find the value of $a$.
15.2 Given that $y=a x^{2}-b x-13$ passes through $(3,8)$, find the value of $b$.

I5.3 If there are $c$ ways of arranging $b$ girls in a circle, find the value of $c$.
I5.4 If $\frac{c}{4}$ straight lines and 3 circles are drawn on a paper, and $d$ is the largest numbers of points of intersection, find the value of $d$.
$$
\begin{array}{l}
\alpha+\beta=2 \alpha \beta \\
-\frac{a}{5}=2\left(-\frac{2}{5}\right) \\
a=4 \\
8=4(3)^{2}-b(3)-13 \\
b=5
\end{array}
$$

First arrange the 5 girls in a line, the number of ways $=5 \times 4 \times 3 \times 2 \times 1=120$ Next, join the first girl and the last girl to form a circle. There are 5 repetitions.
The number of ways $=c=120 \div 5=24$
For the 3 circles, there are 6 intersections.
If each straight line is drawn not passing through these intersections, it intersects the 3 circles at 6 other points. The 6 straight lines intersect each other at $1+2+3+4+5$ points.
$\therefore d=$ the largest numbers of points of intersection $=6+6 \times 6+15=57$