Find Polynomial Equation: 3 Zeros, f(2)=91

[red_raider]

I need to find the polynomial equation. The givens are: n=3; -5 and 4+3i are zeros; f(2)=91
I have no idea how to find this? Can you please help

 

[grief]

is n the degree of the polynomial?

Hint: if 4+3i is a zero, then 4-3i is a zero.

So you know that your polynomial is of the form c*(x+5)(x-4-3i)(x-4+3i), where c is some constant.

Now you need to figure out what c is.

 

[HallsofIvy]

grief is also assuming that all coefficients are real numbers. It is also possible to have a polynomial with complex coefficients but then the information given would not be enough to determine the polynomial.

 

[statdad]

"grief is also assuming that all coefficients are real numbers. It is also possible to have a polynomial with complex coefficients but then the information given would not be enough to determine the polynomial."

I must be misunderstanding: both by hand and with Scilab I obtain specific real and complex parts for a polynomial that has the o.p.'s specifications (zeros and value for x = 0). It would seem that the "initial condition" nails down the leading coefficient, and the factors that correspond to the zeros do the rest.

I've been grading all afternoon, so am rather zonked. What simple thing am I missing?