Question 104483: Hello,
I have the following multiple choice question:
Find an nth degree polynomial function with real coefficients satisfying the given conditions.
n = 3; - 4 and i are zeros; f(-3) = 60
A) f(x) = 6 + 24 + 6x + 24
B)
f(x) = -6 - 24 + 6x + 24
C)
f(x) = 6 + 24 - 6x - 24
D)
f(x) = -6 - 24 - 6x - 24
I'm not sure if I'm supposed to substitute the values into the multiple choices to see which one works out. Regardless, I would like to find the answer on my own without having to plug the values in. Could you help me? I looked in my algebra book but I couldn't find a section for this. I would greately appreciate it if someone could give me some direction.
Thank you,
EJ
Answer by Fombitz(32388)   (Show Source):
You can put this solution on YOUR website! EJ, let's start with what you know.
Nth degree polynomial with n=3 means
Your job is to find a,b,c,d with the rest of the information provided.
The problems is you have 4 unknowns (a,b,c,d) and only three equations to solve them with. Let's plug in and see what we find.
1.
2.
3.
Simplifying the equations, gives you
1.
2. 
3.
where  and  .
Since you have a complex expression in your second equation, it actually acts as an additional equation. Since both the real part and the complex part of equation 2 have to equal zero, you now have 4 equations with four unknowns.
1.
2.(Real)
3.(Complex)
4.
With those 4 equations, you are able to substitute and find the values for a,b,c,d.
Good luck and post another question if you get stuck.
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