SOLUTION: Find a polynomial with integer coefficients that has degree 4, zeros 5i and 1+i, and constant term 150.

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Find a polynomial with integer coefficients that has degree 4, zeros 5i and 1+i, and constant term 150.      Log On


   

Question 1155518: Find a polynomial with integer coefficients that has degree 4, zeros 5i and 1+i, and constant term 150.
Answer by josgarithmetic(39626) About Me  (Show Source):
You can put this solution on YOUR website!
Start with y=a%28x-5i%29%28x%2B5i%29%28x-%281%2Bi%29%29%28x-%281-i%29%29, and simplify.

Doing the multiplying carefully, and understanding that i%5E2=-1,
the steps should yield y=a%28x%5E2%2B25%29%28x%5E2-2x%2B2%29, which is not yet fully multiplied.

Constant term of 150 means that if x is one of the zeros, then y is 150. Use this to find "a".