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Math Help - [SOLVED] Polynomial Problem

  1. #1
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    [SOLVED] Polynomial Problem

    Consider two distinct polynomials of degree N:


    A(X) = a0 + a1*X + a2*X^2 + … + aN*X^N

    B(X) = b0 + b1*X + b2*X^2 + … + bN*X^N

    where ak and bk are real numbers. Suppose that at X = 1, 2, ..., N, the graphs of A(X) and B(X) intersect.

    Questions:

    1.) At what places besides X = 1, 2, ..., N do the graphs of A and B intersect?

    2.) What is (a0 – b0)/(aN – bN) ?
    Last edited by mr fantastic; April 1st 2009 at 02:06 AM. Reason: Restored question deleted by OP.
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  2. #2
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    Quote Originally Posted by dxdy View Post
    Consider two distinct polynomials of degree N:


    A(X) = a0 + a1*X + a2*X^2 + + aN*X^N

    B(X) = b0 + b1*X + b2*X^2 + + bN*X^N

    where ak and bk are real numbers. Suppose that at X = 1, 2, ..., N, the graphs of A(X) and B(X) intersect.

    Questions:

    1.) At what places besides X = 1, 2, ..., N do the graphs of A and B intersect?
    they can't intersect in anywhere else because otherwise A(x)-B(x) must be a polynomial of degree at least n+1 and that is obviously false.

    2.) What is (a0 b0)/(aN bN) ?
    A(x)-B(x)=(a_n - b_n)x^n + \cdots + a_0 - b_0 and x=1,2, \cdots , n are the roots of A(x)-B(x). therefore: \frac{a_0 - b_0}{a_n - b_n}=(-1)^n n!.
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