Thread: Polynomial and Rational Functions

Hello, I have a few questions that I'm stuck on, not sure what to do.

First one says to: Form a polynomial f(x) with real coefficients having tghe given degree and zeros.

1.) Degree 4; zeros: 3 +2i; 4, Multiplicity 2

The next one says to find the complex zeros of each polynomial function. Write F in factored form.

2.) f(x) = x^3 - 8x^2 + 25x -26

Thanks alot everyone!!

[QUOTE=MathMack;311940]Hello, I have a few questions that I'm stuck on, not sure what to do.

First one says to: Form a polynomial f(x) with real coefficients having tghe given degree and zeros.

1.) Degree 4; zeros: 3 +2i; 4, Multiplicity 2[quote]
In order to have real coefficients, the 3+ 2i root must be paired with 3- 2i so you want roots 3+ 2i, 3- 2i, 2, 2. The polynomial is (x- (3+ 2i))(x-(3-2i))(x- 2)(x- 2)= (x- 3-2i)(x-3+2i)(x-2)(x-2). Multiply that out.

[quote]The next one says to find the complex zeros of each polynomial function. Write F in factored form.

2.) f(x) = x^3 - 8x^2 + 25x -26

I notice that so x= 2 is one root. Dividing by x- 2, we get . Now complete the square. Write so , , . The roots are x= 2, x= 3+ 2i, and x= 3- 2i. The factored form is (x- 2)(x- 3- 2i)(x- 3+ 2i).
(x- 3
Thanks alot everyone!!

Originally Posted by MathMack

Hello, I have a few questions that I'm stuck on, not sure what to do.

First one says to: Form a polynomial f(x) with real coefficients having tghe given degree and zeros.

1.) Degree 4; zeros: 3 +2i; 4, Multiplicity 2

The next one says to find the complex zeros of each polynomial function. Write F in factored form.

2.) f(x) = x^3 - 8x^2 + 25x -26

Thanks alot everyone!!

What do you mean by "Multiplicity 2"?