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baegelion wrote:5. What is the maximum degree of a polynomial of the form
with for 0 ≤ i ≤ n, 1 ≤ n, such that all the zeros are real?Some clarification is required about
since just the second degree expression has complex zero.
x^2 - x - 1 also fits the form and has two positive zeroes.
#4 is not 1.
4. Suppose we have the following identity:
5. What is the maximum degree of a polynomial of the form
with for 0 ≤ i ≤ n, 1 ≤ n, such that all the zeros are real?6. Let f(m,1) = f(1,n) = 1 for m ≥ 1, n ≥ 1, and let f(m,n) = f(m-1,n) + f(m,n-1) + f(m-1,n-1) for m > 1 and n > 1. Also, let
1. Let F(x) be the real-valued function defined for all real x except for x = 0 and x = 1 and satisfying the functional equation F(x) + F((x-1)/x) = 1+x. Find the F(x) satisfying these conditions.
Write F(x) as a rational function with expanded polynomials in the numerator and denominator.
2. Suppose that f(x) and g(x) are functions which satisfy f(g(x)) = x^2 and g(f(x)) = x^3 for all x ≥ 1. If g(16) = 16, then compute log_2 g(4). f(x) ≥ 1 and g(x) ≥ 1 for all x ≥ 1
3. The function
satisfies xf(x) + f(1 - x) = x^3 - x for all real x. Find f(x).Pages: 1