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

1 Answer
Dec 26, 2015

Answer:

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#.