SOLUTION: Find a polynomial of degree 4 with integer coefficients has zeros 1+i and i, with constant term 6. What is the leading coefficient?

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: Find a polynomial of degree 4 with integer coefficients has zeros 1+i and i, with constant term 6. What is the leading coefficient?      Log On


   

Question 1071910: Find a polynomial of degree 4 with integer coefficients has zeros 1+i and i, with constant term 6. What is the leading coefficient?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Real coefficients in a polynomial with complex roots means the roots come in complex conjugate pairs,
f%28x%29=a%28x-%281%2Bi%29%29%28x-%281-i%29%29%28x-i%29%28x%2Bi%29
f%28x%29=a%28x%5E2-2x%2B2%29%28x%5E2%2B1%29
f%28x%29=a%28x%5E4-2x%5E3%2B3x%5E2-2x%2B2%29
So then,
2a=6
a=3
highlight%28f%28x%29=3%28x%5E4-2x%5E3%2B3x%5E2-2x%2B2%29%29