Writing factored form equations with complex zeros at 3, 0, -9±4i

[Erin_Sharpe]

I'm taking a correspondence course to upgrade my marks for admission to a program.. and since its all teach yourself, I'm having some trouble on this particular question:

Write an equation in factored form for the family of functions having non-repeated zeros at 3, 0, -9 +4i and -9-4i

AND

write in factored form, the equation of a specific member of this family of functions.


Keep in mind guys that I'm not trying to do my homework on here, I just could really use some help!
Thanks!
Erin

 

[dextercioby]

I'll give u the general formula
$$y(x)=a(x-x_{1})(x-x_{2})(x-x_{3})(x-x_{4})$$
,where "a" is a parameter (the one that gives the idea of 'family of functions'),and $x_{i}$ are the roots of the polynomial 'y',else,the zero-s of the function 'y'.

It's good if $a\neq 0$.

Daniel.

 

[Erin_Sharpe]

Thank you! Thank you!