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
-
UP 0 DOWN 0 0 2
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...