SOLUTION: use the cubic function f(x)=x^3+x^2-3x+1 to complete the remaining problems 1) what are the possible roots of this function 2)test your possibilities synthetically to d

Algebra ->  Rational-functions -> SOLUTION: use the cubic function f(x)=x^3+x^2-3x+1 to complete the remaining problems 1) what are the possible roots of this function 2)test your possibilities synthetically to d      Log On


   

Question 465261: use the cubic function f(x)=x^3+x^2-3x+1 to complete the remaining problems 1) what are the possible roots of this function 2)test your possibilities synthetically to determine which one(s) is(are) valid
Found 2 solutions by stanbon, ewatrrr:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
use the cubic function f(x)=x^3+x^2-3x+1 to complete the remaining problems
---------------------
1) what are the possible roots of this function
Possible roots: +1 and -1
---------------------------
2)test your possibilities synthetically to determine which one(s) is(are) valid
-----
1)....1....1....-3....1
.......1....2....-1...|..0
Quotient: x^2+2x-1
Remainder: 0
----
The root is x = 1.
---
Note: Notice that the coefficients of the cubic add
up to zero. That tells you x = 1 is a root.
====================================================
Cheers,
Stan H.

Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi,

 f(x)=x^3+x^2-3x+1 | x = 1 is a root, 1+1-3+1 = 0

%28x%5E3%2Bx%5E2-3x%2B1%29%2F%28x-1%29 = x^2+2x-1 = (x+1)^2-2 , x = -1%2B-sqrt%282%29

-2.414,.414,1 possible roots