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Math Help - No. of real roots.

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    No. of real roots.

    Let f(x) be a polynomial of degree n, an odd positive integer, and has monotonic behaviour , then the number of real roots of the equation
    f(x)+f(2x)+......+f(nx) = \frac{1}{2} n(n+1) is equal to
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  2. #2
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    I think the point is that f(x) is monotonic means that f(kx) is monotonic in the same direction (increasing/decreasing).

    The sum of of monotonic functions in the same direction is monotonic.

    How many real roots can a monotonic function have?
    E.g. how many times can a strictly increasing function intersect the x-axis?
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  3. #3
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    Quote Originally Posted by snowtea View Post
    I think the point is that f(x) is monotonic means that f(kx) is monotonic in the same direction (increasing/decreasing).

    The sum of of monotonic functions in the same direction is monotonic.

    How many real roots can a monotonic function have?
    E.g. how many times can a strictly increasing function intersect the x-axis?
    one solution.

    Thanks.
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