Home
Class 12
MATHS
Let n be a natural and let 'a' be a real...

Let n be a natural and let 'a' be a real number. The number of zeros of `x^(2n+1)-(2n+1)x+a=0` in the interval `[-1,1]` is -

A

2 if a gt 0

B

2 if a lt 0

C

At most one for every value of a

D

At least three for every value of a

Text Solution

Verified by Experts

The correct Answer is:
C
`f(x)=x^(2n+1)-(2n+1)x+a`
`f'(x)=(2n+1)x^(2n)-(2n+1)`
`=(2n+1)(x^(2n)-1)le0` when x `in[-1,1]`
f(x) is strictly decreasing in `[-1,1]`
f(x) cut x axis at most one point in given interval
Promotional Banner

Similar Questions

Explore conceptually related problems

Let n be an odd natural number greater than 1.Then,find the number of zeros at the end of the sum 99^(n)+1.

The maximum number of real roots of the equation x^(2n) -1 = 0 , is

Let n be a natureal number and 0ltxlt1 Statement 1: The coefficient of x^(n) in log (1)/(1+x+x^(2)) is (1)/(n) when n is not a multiple of 3 Statement 2: The coefficient of x^(n) in log(1)/(1-x+x^(2)-x^(3)) is (1)/(n) when n is an odd natural number

Let x_(1),x_(2),x_(n) values of variable X and let 'a' be non zero real number.Then prove that the variance of the observations ax_(1),ax_(2),*ax_(n) is a^(2)Var(X). Also,find their standard deviation.

Let P(n) be a statement and let P(n) Rightarrow P(n+1) for all natural number n, then P(n) is true.

let 'n' be any odd natural number. Choose the incorrect statement about the number n(n^(2)-1)

Let f_1 : (0, oo) to R and f_2 : (0, oo) to R be defined by f_1(x) = int_0^xprod_(j= 1)^21((t − j)^j)dt, x gt 0 and f_2(x) = 98(x − 1)^50 − 600(x − 1)^49 + 2450, x gt 0 , where, for any positive integer n and real numbers a_1, a_2, … , a_n, prod_(i=1)^n(a_i) denotes the product of a_1 , a_2, … , a_n . Let m_i and n_i , respectively, denote the number of points of local minima and the number of points of local maxima of function f_i, i = 1, 2 , in the interval (0, oo) The value of 2m_1+3n_1+m_1n_1 is ___.

Let f_1 : (0, oo) to R and f_2 : (0, oo) to R be defined by f_1(x) = int_0^xprod_(j= 1)^21((t − j)^j)dt, x gt 0 and f_2(x) = 98(x − 1)^50 − 600(x − 1)^49 + 2450, x gt 0 , where, for any positive integer n and real numbers a_1, a_2, … , a_n, prod_(i=1)^n(a_i) denotes the product of a_1 , a_2, … , a_n . Let m_i and n_i , respectively, denote the number of points of local minima and the number of points of local maxima of function f_i, i = 1, 2 , in the interval (0, oo) The value of 6m_2+4n_2+8m_2n_2 is ___.

Let nge1, n in Z . The real number a in 0,1 that minimizes the integral int_(0)^(1)|x^(n)-a^(n)|dx is