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Math Help - Find Polynomial of lowest degree w/ zeros

  1. #1
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    Find Polynomial of lowest degree w/ zeros

    A polynomial of lowest degree with real coefficients which has 2, 31/2 , 2i, and 3i as zeroes would be of degree

    For this one I had no clue, I thought it was 4, but it was 6. What's the rule here?
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  2. #2
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    Quote Originally Posted by nandokommando View Post
    A polynomial of lowest degree with real coefficients which has 2, 31/2 , 2i, and 3i as zeroes would be of degree

    For this one I had no clue, I thought it was 4, but it was 6. What's the rule here?
    Hi nandokommando,

    For any polynomial function, if an imaginary number is a zero of that function, its conjugate is also a zero.

    Zeros = {2, 31/2, +2i, -2i, +3i, -3i}
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    Quote Originally Posted by nandokommando View Post
    A polynomial of lowest degree with real coefficients which has 2, 31/2 , 2i, and 3i as zeroes would be of degree

    For this one I had no clue, I thought it was 4, but it was 6. What's the rule here?
    As masters said, if a polynomial with real coefficients has a+ bi as zero it must also have it's complement, a- bi, as zero. A polynomial with real coefficients have 2, 31/2, 2i and 3i as zeros must also have -2i and -3i as zeros and so is of the form a(x- 2)(x- 31/2)(x- 2i)(x- 3i)(x+ 2i)(x+ 3i) and is degree 6.
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