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Math Help - Zeros of a function

  1. #1
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    Zeros of a function

    Okay, I fully understand that complex zeros exist in conjugate pairs, but what about irrational zeros; it would appear as though this would apply to them as well. Am I mistaken?

    Also, how do you find the coefficients of of the leading terms of a rational function? Would I substitute an x and y value in and solve in the form of: y=a_1(x-b)/a_2(x-c), where b and c are the constants, and a_1 and a_2 are the leading coefficients, which I would solve individually?

    Thank you
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  2. #2
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    Re: Zeros of a function

    Quote Originally Posted by Bashyboy View Post
    Okay, I fully understand that complex zeros exist in conjugate pairs, but what about irrational zeros; it would appear as though this would apply to them as well. Am I mistaken?

    for your 1st question ...Math Forum - Ask Dr. Math

    Also, how do you find the coefficients of of the leading terms of a rational function? Would I substitute an x and y value in and solve in the form of: y=a_1(x-b)/a_2(x-c), where b and c are the constants, and a_1 and a_2 are the leading coefficients, which I would solve individually?
    ... can you provide a specific example of what you're looking for in your second question?
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  3. #3
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    Re: Zeros of a function

    For a polynomial with integer coefficients, the irrational zeros do not have to occur in conjugate pairs. If there are exactly two irrational zeros, they will be a conjugate pair.
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