If `x`_{1}, `x`_{2} are the roots of a quadratic
polynomial `x`^{2} + `ax` + `b`, then we have

(`x` - `x`_{1})(`x` - `x`_{2}) = `x`^{2}
+ `ax` + `b`.

By expanding the left side and compare with the right side, we get

`a` = - (`x`_{1} + `x`_{2}), `b` = `x`_{1}`x`_{2.}

Since the polynomial is specified by the two coefficients `a` and `b`,
we see that the transformation

roots (`x`_{1}, `x`_{2}) → polynomial `x`^{2}
+ `ax` + `b`

is essentially the same as

**R**^{2} → **R**^{2}, (`x`_{1},
`x`_{2}) → (`x`_{1} + `x`_{2},
`x`_{1}`x`_{2})

As an exercise for yourself, how would you define the transformation `Root-Polynomial`:
**R**^{3} → **R**^{3} for three roots of polynomials
of degree 3?

Finally, you may try the general case `Root-Polynomial`: **R**^{n}
→ **R**^{n}.