Finding Polynomial Equation

106
0
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.
 

Hurkyl

Staff Emeritus
Science Advisor
Gold Member
14,829
14
You only need to include the complex conjugates if you are looking for a real polynomial; they're not necessary for complex polynomials.
 

The Physics Forums Way

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving
Top