Split the middle term by computer

You will write a function that finds the split of the middle term, use it to get the roots, and solve a problem about a photograph.

The idea. For $ax^2 + bx + c$ you need $p$ and $q$ with $p + q = b$ and $p \times q = a \times c$. Then $ax^2 + bx + c = \dfrac{(ax + p)(ax + q)}{a}$, so the roots are $-\dfrac{p}{a}$ and $-\dfrac{q}{a}$.

Your tasks.

1. In split, return the pair (p, q) of whole numbers, with p <= q, or None when there is no such pair.
2. In roots, return the two roots, smallest first, using split. Return an empty list when there is no split.
3. A photograph is $4\ \text{cm}$ longer than it is wide, and its area is $77\ \text{cm}^2$. Its width $w$ solves $w^2 + 4w - 77 = 0$. Set width to the root that makes sense.