SOLUTION: Construct a fifth degree polynomial p(x) with real coefficients so that the numbers -1, 5 and 3 + i are all roots of p(x).

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Construct a fifth degree polynomial p(x) with real coefficients so that the numbers -1, 5 and 3 + i are all roots of p(x).       Log On


   

Question 1028749: Construct a fifth degree polynomial p(x) with real coefficients so that the numbers
-1, 5 and 3 + i are all roots of p(x).
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
You don't provide enough information to solve.
You need 5 roots.
You provided 4 roots (complex conjugate is also a root since coefficients are real).
You could have multiplicity of 2 for the real roots so there may be two possible solutions,
f%28x%29=%28x%2B1%29%5E2%28x-5%29%28x-%283%2Bi%29%29%28x-%283-i%29%29
f%28x%29=%28x%2B1%29%5E2%28x-5%29%5E2%28x-%283%2Bi%29%29%28x-%283-i%29%29
But I don't think that's the solution you're looking for.
Please repost with additional information.