Question

Is it possible to factor `y= - x^2 - 10x + 20`? If so, what are the factors?

Answer 1

It's possible to factor this polynomial in `RR` as `-(x + 5 - 3sqrt5)(x + 5 + 3sqrt5)`

Explanation:

We need to calculate `Delta = b^2 - 4ac` in order to find the roots.

Here, `Delta = 100 -4*(-1)*20 = 180 > 0` so it has 2 real roots.

The quadratic formula tells us that the solutions are `(-b +- sqrtDelta)/2a`. Here, `sqrtDelta = sqrt180 = 6sqrt5`

`x_1 = (10 - 6sqrt5)/-2 = (6sqrt5 - 10)/2 = 3sqrt5 - 5` and `x_2 = (-10 - 6sqrt5)/2 = -5 - 3sqrt5`.