quartic polynomial

[xc630]

The probblem states a quartic polynomial P (x) with real coeefiecients has zeros 2+i and 3-2i. I think the other zeroes would be 2-i and 3+2i. The next step is if P (0)= 13, then find a rule for P (x). I don't know how to do this. I would appreciate any help.

 

[tkhunny]

I do not quite understand the question.

You have correctly determined the other two zeros. This COMPLETELY defines a unique Quartic Polynomial. After that, P(0) = 13 would only be by coincidence or luck. So, what is the question?

 

[xc630]

ok here is the question

A quartic polynomial P(x) with real coeffiecients has zeros 2 + i and 3-2i.

Then it goes on to part A

a. Find the other zeros (whihc I did)

Then it skips to part C

c. If P (0) = 13, find a rule for P (x)

I have no idea how to do that.

 

[tkhunny]

Since your quartic polynomial is already completely defined in Part A, and
Since P(0) = 65 from Part A,

I would say the rule for P(x),
given that P(0) = 13 is:

"Such a P(x) doesn't exist".

It all seems very odd. I wonder what Part B contained?