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Math Help - Constucting cubic function from given complex zeros.

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    Constucting cubic function from given complex zeros.

    Hi, The question is Write down a polynomial of degree 3, whose coefficients are all real, that has 4i and 2 as two of its zeros.

    please help can you try to solve this. i got no clue
    Last edited by mr fantastic; February 21st 2011 at 10:30 AM. Reason: Re-titled.
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    If you are asked to write down , for example, a polynominal of degree 2 that has 2 and 3 as its zeros, you will find;
    f(x) = (x-2)(x-3)
    by substituting either x=2 or x=3, it's clear this satisfies the question.

    Similarly,....

    + if an polynominal f(x)=0 <whose coefficient is all real> has an complex root, x = a+bi, (a and b are real), we can say...
    Last edited by joll; February 21st 2011 at 01:04 AM. Reason: adding the < > part
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    Quote Originally Posted by Barney View Post
    Hi, The question is Write down a polynomial of degree 3, whose coefficients are all real, that has 4i and 2 as two of its zeros.

    please help can you try to solve this. i got no clue
    1. Let x denote the variable.

    2. If x = 4i is a solution then x = -4i must be a solution too, otherwise all coefficient can't be real.

    3. Now you can calculate the LHS of the equation:

    (x-2)(x-4i)(x+4i)=0

    4. Expand the LHS. Collect like terms. That's all.
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