Question

Rozwiąż -x7-2x6-x5+2x4+2x3=0 to co stoi przy x to potęga ;)

Answer 1

-x7-2x6-x5+2x4+2x3=0

-x3(x4+2x3+x2-2x-2)=0

 

(x4+2x3+x2-2x-2):(x-1)=x3+3x2+4x+2

-x4+x3

-------------

......3x3+x2

......-3x3+3x2

----------------------

.............4x2-2x

.............-4x2+4x

--------------------------

.....................2x-2

.......................-2x-2

---------------------------------

========================

 

-x3(x-1)(x3+3x2+4x+2)=0

 

(x3+3x2+4x+2):(x+1)=x2+2x+2

-x3-x2

-------------

......2x2+4x

......-2x2-2x

----------------

.............2x+2

............-2x-2

-----------------------

==================

 

-x3(x-1)(x+1)(x2+2x+2)=0

 

x2+2x+2=0

delta=4-8=-4    - nie ma pierwiastków

 

odp.  x=0 lub x=1 lub x=-1