SOLUTION: find the roots of the polynomial p(x) = x^4+4x^3+6x^2+4x+5=0 given that one of the roots is x= -1

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: find the roots of the polynomial p(x) = x^4+4x^3+6x^2+4x+5=0 given that one of the roots is x= -1      Log On


   

Question 976062: find the roots of the polynomial
p(x) = x^4+4x^3+6x^2+4x+5=0 given that one of the roots is x= -1
Answer by josgarithmetic(39623) About Me  (Show Source):
You can put this solution on YOUR website!
Synthetic Division gives this:


________________|________
_______________|
_______-1______|________1______4______6_______4_______5
_______________|_______________-1____-3_______-3_____-1
_______________|__________________________________________
_______________________1______3_______3_______1______4

NO. The remainder is not 0. x=-1 IS NOT a root.

Try testing for x=-5 and continue from there.
_______________|
_______-5______|________1______4______6_______4_______5
_______________|_______________-5____10_______-80_____380
_______________|__________________________________________
_______________________1______-2_______16______-76______385

NOT a root or zero either.


Using software for graphing to make a fast check, your function p(x) has NO REAL zeros!!!