1thanks shubhodip
Let f(x) be the monotonic polynomial of (2m-1) degree where m belongs to natural no., then equation f(x)+f(3x)+f(5x)+. . . . . .f((2m-1)x) = 2m-1 has:
A) At least one real root
B) (2m-1) real roots
C) exactly one real root
D) none of these
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2 Answers
21monotonic polynomial must be of odd degree, and will be equal to all real numbers for exactly one value of x. g(x) = f(x) + f(3x) + ... + f((2m-1)x) is also monotonic, so g(x) = 2m-1 has exactly one real root...