Help Me, please.
Roots: find the square roots of the following polynomials.
4a2 + 20ab +25b2 + 4ac - 10bc + c2
4a^2 + 20ab +25b^2 + 4ac - 10bc + c^2
The factorization of this isn't easy to see, Manuel....it is this :
(2a + 5b - c) ( 2a + 5b - c )
We can can check this by distibuting each term in the first set of parentheses over the terms in the second set of parentheses
4a^2 + 10ab - 2ac
+ 10ab + 25b^2 - 5bc
- 2ac - 5bc + c^2
4a^2 + 20ab - 4ac + 25b^2 - 10bc + c^2
So....the factorization is
( 2a + 5b + c)^2
And taking both roots of this we have
±√(2a + 5b - c )