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Math Help - polynomials and zeros

  1. #1
    paladin123
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    polynomials and zeros

    How do you solve these?? Have been puzzling over them since Monday. I need to pass this 8 hrs from now. Thanks!

    1) R is a root of f(x)=x^2+x+1; what is the remainder when P(x)= x^3333-x^333+x^33-x^3+3 is divided by x/r?

    2) What is the domain of the 1-to-1 function f(x)= 2^x/2 - 3; find the inverse function and its range. Then, show that the composite functions f(f^1(x)) and f^1(f(x)) are both equal to x.
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  2. #2
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    Quote Originally Posted by paladin123 View Post

    1) R is a root of f(x)=x^2+x+1; what is the remainder when P(x)= x^3333-x^333+x^33-x^3+3 is divided by x/r?
    .
    What is R?
    By Quadradic Forumula,
    x=[(-1)+/-isqrt(3)]/2

    Let us say that,
    R=(-1/2)+(sqrt(3)/2)i
    The "-" should give the same result.

    Now express in polar coordinates,
    cos(5pi/6)+i*sin(5pi/6)

    Now you can easily compute what 3333,333,33,3
    Given when raised to their power through de-Moiver's theorem.

    2) What is the domain of the 1-to-1 function f(x)= 2^x/2 - 3; find the inverse function and its range. Then, show that the composite functions f(f^1(x)) and f^1(f(x)) are both equal to x.
    Use paranthesis!
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