Finding a polynomial function given this info.. Here is my work

[Elizabeth083]

Hello,

The question is: Find the least degree polynomial function with zeroes: -1-3i, and 4 with a multiplicity of 4.
And, f(0)=215.

I understand the factors to thus be: (x-4)^4, and (x+(-1-3i)) and (x+(-1+3i)).

I simplify to get this: f(x)=(x-4)^4(x-1-3i)(x-1+3i)

But another aspect of the question is the Y intercept, because it says the function must contain f(0)=215. I'll call the missing value for this "a".
So to find A, I do this:

215=a (0-4)^3) (0-1-3i) (0-1+3i)

And I get A= 0.083984375

so final function: f(x)=0.083984375((x-4)^4 (x-1-3i) (x-1+3i)

Have I made mistakes?

 

[AmandasMathHelp]

Good job using the complex conjugate as well as the -1-3i root. But in your terms you need to subtract the roots, not add them. so..

[MATH](x-(-1-3i))(x-(-1+3i))=(x+1+3i)(x+1-3i)[/MATH]
One thing I like to do with complex terms like this is multiply them together because you'll get a nice x^2+bx+c expression and get rid of the imaginary numbers. I'll let you try that! Also your A value is correct but if you can I would leave it as a fraction and not a super long decimal. You should be able to get 215=a*2560 if you simplify and just leave it as A=215/2560=43/512

 

[Elizabeth083]

43/512(x^6-14x^5+74x^4-224x^3+704x^2-2048x+2560)

is equal to:



that's after multiplying the factors out.. still a monster hehe. Thanks for your help!