SOLUTION: Hey, If you could help me remember how to do this type of problem it would be AWESOME! Form a polynomial degree with real coefficients so that 2+i and -1 are zeros. Thanks

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Hey, If you could help me remember how to do this type of problem it would be AWESOME! Form a polynomial degree with real coefficients so that 2+i and -1 are zeros. Thanks      Log On


   

Question 490706: Hey,
If you could help me remember how to do this type of problem it would be AWESOME!
Form a polynomial degree with real coefficients so that 2+i and -1 are zeros.
Thanks!
(Answer is x^3-3x^2+x+5; just need to know how to figure this out - thanks!
Answer by John10(297) About Me  (Show Source):
You can put this solution on YOUR website!
We know this polynomial has at least 3 solutions which are (2 + i), (2 - i) and -1
Thus we apply the formula (x - a)(x - b)(x - c)= 0 where a,b, and c are given solutions.
(x - 2 - i)(x - 2 + i)(x + 1) = 0
Use the distributive to multiply from left to right
(x^2 - 2x + xi - 2x +4 - 2i - xi + 2i - i^2)(x + 1) = 0
Simplify
(x^2 - 4x + 5)(x + 1) = 0
x^3 + x^2 - 4x^2 - 4x + 5x + 5 = 0
x^3 - 3x^2 + x + 5 = 0
The LEFT SIDE is what you are looking for.
John10:)