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Math Help - Planet Venus

  1. #1
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    Write A Polynomial Function

    Write a polynomial function of least degree that has real coefficients, the given zeros and a leading coefficient of 1.
    4, -4, -3i
    Last edited by magentarita; December 22nd 2008 at 06:24 AM. Reason: changed question
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  2. #2
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    Quote Originally Posted by magentarita View Post
    Write a polynomial function of least degree that has real coefficients, the given zeros and a leading coefficient of 1.
    4, -4, -3i
    You can solve polynomial equations by factoring right? If p(x)= (x-a)(x-b)(x-c) then x= a, x= b, and x= c are the zeros. And the fact that the coefficient of each x is 1 means that the leading coefficient after you have multiplied it out will be 1. The answer to the problem as you have stated it is (x- 4)(x+ 4)(x+ 3i).

    WARNING! You did NOT say that the polynomial must have real coefficients! For example, the constant term of that would be -48i. If you are also required to have real coefficients you will need the "complex conjugate" also as a zero: (x-4)(x+4)(x+ 3i)(x-3i).
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  3. #3
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    ok..........

    Quote Originally Posted by HallsofIvy View Post
    You can solve polynomial equations by factoring right? If p(x)= (x-a)(x-b)(x-c) then x= a, x= b, and x= c are the zeros. And the fact that the coefficient of each x is 1 means that the leading coefficient after you have multiplied it out will be 1. The answer to the problem as you have stated it is (x- 4)(x+ 4)(x+ 3i).

    WARNING! You did NOT say that the polynomial must have real coefficients! For example, the constant term of that would be -48i. If you are also required to have real coefficients you will need the "complex conjugate" also as a zero: (x-4)(x+4)(x+ 3i)(x-3i).
    That was easy. Thanks!
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