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Math Help - Polynomial and Rational Functions

  1. #1
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    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!!
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  2. #2
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    [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 2^3- 8(2^2)+ 25(2)- 26= 8- 32+ 50- 26= 58- 58= 0 so x= 2 is one root. Dividing by x- 2, we get x^2- 6x+ 13. Now complete the square. Write x^2- 6x+ 13= x^2- 6x+ 9- 9+ 13= (x- 3)^2- 4= 0 so (x- 3)^2= -4, x- 3= \pm 2i, x= 3\pm 2i. 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!!
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  3. #3
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    Quote Originally Posted by MathMack View Post
    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"?
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