Polynomial function

[Cake]

Hey Guys,


So they are asking me to write a polynomial function, p(x), with real coefficients having the given characteristics.
Degree 4
Zeros: -3(Multiplicity 2), 2- i
p(2) = 20

I have formed the function:
(x+3)^2(x-2-i)(x-2+i)

I understand how to form the function but I don't a clue on how to do the "p(2) = 20".
I need help setting it up or knowing how to solve it.

 

[HallsofIvy]

Hey Guys,


So they are asking me to write a polynomial function, p(x), with real coefficients having the given characteristics.
Degree 4
Zeros: -3(Multiplicity 2), 2- i
p(2) = 20

I have formed the function:
(x+3)^2(x-2-i)(x-2+i)[/tex]

That is one possible solution. But \(\displaystyle a(x+ 3)^3(x- 2- i)(x- 2+ i)\) will have the given zeros for any number a.

I understand how to form the function but I don't a clue on how to do the "p(2) = 20".
I need help setting it up or knowing how to solve it.

When x= 2, \(\displaystyle a(x+ 3)^2(x- 2- i)(x- 2+ i)= a(5^2)(-i)(i)= 25a\). Set that equal to 20 and solve for a.

 

[Cake]

That is one possible solution. But \(\displaystyle a(x+ 3)^3(x- 2- i)(x- 2+ i)\) will have the given zeros for any number a.


When x= 2, \(\displaystyle a(x+ 3)^2(x- 2- i)(x- 2+ i)= a(5^2)(-i)(i)= 25a\). Set that equal to 20 and solve for a.

Perfect, that makes complete sense.

Thanks, Ivy.