SOLUTION: Find all the zeros of the function. f(x)=x^4+2x^3-7x^2+2x-8

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Find all the zeros of the function. f(x)=x^4+2x^3-7x^2+2x-8      Log On


   

Question 695353: Find all the zeros of the function.
f(x)=x^4+2x^3-7x^2+2x-8
Found 2 solutions by Alan3354, MathLover1:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Find all the zeros of the function.
f(x)=x^4+2x^3-7x^2+2x-8
-----------------------
Try the factors of 8 first, 1, 2, 4 & 8
Plus and minus.

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29=x%5E4%2B2x%5E3-7x%5E2%2B2x-8....factor it
set f%28x%29=0
replace 2x%5E3 with 4x%5E3-2x%5E3 and -7x%5E2 with x%5E2-8x%5E2

x%5E4%2B4x%5E3-2x%5E3%2Bx%5E2-8x%5E2%2B4x-2x-8..group
%28x%5E4%2B4x%5E3%29-%282x%5E3%2B8x%5E2%29-%28x%5E2%2B4x%29-%282x%2B8%29=0
x%5E3%28x%2B4%29-2x%5E2%28x%2B4%29-x%28x%2B4%29-2%28x%2B4%29=0
%28x%5E3-2x%5E2-x-2%29%28x%2B4%29=0
%28%28x%5E3-2x%5E2%29-%28x-2%29%29%28x%2B4%29=0
%28x%5E2%28x-2%29-%28x-2%29%29%28x%2B4%29=0
%28x%5E2%2B1%29%28x-2%29%28x%2B4%29=0

solutions:
if x%5E2%2B1=0...=>...x%5E2=-1.=>...x=sqrt%28-1%29....two complex solutions: i and -i
if x-2=0 ...=>...x=2....real solution
if x%2B4=0 ...=>...x=-4...real solution

+graph%28+600%2C+600%2C+-10%2C10%2C+-50%2C+10%2Cx%5E4%2B2x%5E3-7x%5E2%2B2x-8%29+