SOLUTION: Write a polynomial equation of least degree with roots of 4, i, -i What happens to the imaginary "I" ?

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Write a polynomial equation of least degree with roots of 4, i, -i What happens to the imaginary "I" ?      Log On


   

Question 701511: Write a polynomial equation of least degree with roots of 4, i, -i
What happens to the imaginary "I" ?
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
you are given three roots, means a polynomial equation of least degree will be a polynomial of third degree

%28x-x%5B1%5D%29%28x-x%5B2%5D%29%28x-x%5B3%5D%29+=0 where x%5B1%5D=4, x%5B2%5D=i, and x%5B3%5D=-i

%28x-4%29%28x-i%29%28x-%28-i%29%29+=0
%28x-4%29%28x-i%29%28x%2Bi%29+=0.....multiply
%28x-4%29%28x%5E2%2Bxi-xi-i%5E2%29+=0...recall i%5E2=-1
%28x-4%29%28x%5E2%2Bcross%28xi%29-cross%28xi%29-%28-1%29%29+=0
%28x-4%29%28x%5E2%2B1%29+=0
x%5E3%2Bx-4x%5E2-4+=0
x%5E3-4x%5E2%2Bx-4+=0