SOLUTION: Sum of the two zeros of a polynomial of degree 4 is -1 and their product is -2. If the other two zeros are root3 and -root3, find the polynomial.

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Sum of the two zeros of a polynomial of degree 4 is -1 and their product is -2. If the other two zeros are root3 and -root3, find the polynomial.      Log On


   

Question 980228: Sum of the two zeros of a polynomial of degree 4 is -1 and their product is -2. If the other two zeros are root3 and -root3, find the polynomial.
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
system%28p%2Bq=-1%2Cpq=-2%29
q=-2%2Fp

p-2%2Fp=-1
p%5E2-2=-p
p%5E2%2Bp-2=0
%28p-1%29%28p%2B2%29=0
If p=1, then q=-2.
These must be the roots.

The polynomial would come in factored form as %28x-1%29%28x%2B2%29%28x-sqrt%283%29%29%28x%2Bsqrt%283%29%29. You can simplify and put into general form.