Caldus
Oct5-03, 12:45 PM
Sorry to keep asking questions...my teacher is horrible...
Anyway, I need to find a polynomial equation with degree 8 and contains the roots (3 - 2i), (-5 + 7i), 0 (with multiplicity 3), -3, and 4 (with multiplicity 2).
This is what I came up with:
p(x) = (x - (3 - 2i))(x - (-5 + 7i))(x)^3(x + 3)(x - 4)^2
Two things I'm wondering about (besides whether I got it right of course):
1. Don't I need to add in the conjugates for 3 - 2i and -5 + 7i in the equation? In that case, the degree would have to be 10, no?
2. Can I simplify this any further?
Thanks again.
Anyway, I need to find a polynomial equation with degree 8 and contains the roots (3 - 2i), (-5 + 7i), 0 (with multiplicity 3), -3, and 4 (with multiplicity 2).
This is what I came up with:
p(x) = (x - (3 - 2i))(x - (-5 + 7i))(x)^3(x + 3)(x - 4)^2
Two things I'm wondering about (besides whether I got it right of course):
1. Don't I need to add in the conjugates for 3 - 2i and -5 + 7i in the equation? In that case, the degree would have to be 10, no?
2. Can I simplify this any further?
Thanks again.