SOLUTION: A polynomial or degree3, with integer coefficients that has zeros root3i and o is : x^3 - 2x^2 + 4x : x^3 - x^2 + xroot3i : 3x^3 - 3x^2 + xi : x^3 + 3x : x^3 - x

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: A polynomial or degree3, with integer coefficients that has zeros root3i and o is : x^3 - 2x^2 + 4x : x^3 - x^2 + xroot3i : 3x^3 - 3x^2 + xi : x^3 + 3x : x^3 - x      Log On


   

Question 1157623: A polynomial or degree3, with integer coefficients that has zeros root3i and o is
: x^3 - 2x^2 + 4x
: x^3 - x^2 + xroot3i
: 3x^3 - 3x^2 + xi
: x^3 + 3x
: x^3 - x^2 + xroot3i

Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
Its other zero is the conjugate of 

sqrt%283%29i
which is
-sqrt%283%29i

So its zeros are 
matrix%281%2C5%2Csqrt%283%29i%2C+%22%2C%22+%2C-sqrt%283%29i%2C+%22%2C%22%2C+0%29 


If a polynomial of degree n has leading coefficient 1, the coefficient of
xn-1 is the -1 times the sum of all zeros.

The sum of all the zeros is 

%28sqrt%283%29i%29%2B%28-sqrt%283%29i%29%2B0

which is 0.

The only choice which has 0 for the coefficient of x² is

x^3 + 3x

Edwin