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Help Me, please.

 

Roots: find the square roots of the following polynomials.

 

4a2 + 20ab +25b2 + 4ac - 10bc + c2

ManuelBautista2019  Feb 2, 2018
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 #1
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+1

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 )     

 

 

 

cool cool cool  

CPhill  Feb 2, 2018
edited by CPhill  Feb 2, 2018

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