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Let f(x) be a monotonic polynomial of (2...

Let f(x) be a monotonic polynomial of (2m-1) degree where `m in N`, then the equation
f(x)+f(3x)+f(5x)+…+f(2m-1)x=(2m-1) has ………… . roots.

A

at least one real root

B

(2m - 1) real roots

C

exactly one real root

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
It is given that f(x) is a monotonic funtion
`therefore f(x) lt 0 or, f(x) gt 0 " for all" x in R`
`rarr f(kx) lt 0 or f(kx) gt 0 " for all " x in R and k in N`
`rArr` f(kx) is also a monotonic function
`rArr f (x) + f(3x) + f(5x)+..+ f((2m -1) ` is monotomic polynomial of degree (2m-1)
`rArr f(x) ` attatins every real value only once
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