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Math Help - polynomials

  1. #1
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    polynomials

    -Use the given zero to find all the zeroes of the function:
    function: f(x)=2x^3+3x^2+50x+75
    zero: 5i



    Thank you!!
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  2. #2
    Member TheMasterMind's Avatar
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    Quote Originally Posted by ss103 View Post
    -Use the given zero to find all the zeroes of the function:
    function: f(x)=2x^3+3x^2+50x+75
    zero: 5i



    Thank you!!
    5i is a zero of f implies that its conjugate -5i is also a zero of f then both (x        - 5i) and (x + 5i) are factors of f and their product x^2        + 25 is a factor of 2x^3 + 3x^2 + 50x + 75
    The quotient 2x^3 + 3x^2 + 50x + 75 is divided by x^2 + 25is 2x + 3

    \therefore f(x) = 2x^3 + 3x^2 + 50x + 75 = (x - 5i)(x        + 5i)(2x + 3) zeros of f are 5i, -5i, and -3/2
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