Home
Class 12
MATHS
Consider the cubic equation f(x)=x^(3)-n...

Consider the cubic equation `f(x)=x^(3)-nx+1=0` where `n ge3, n in N` then `f(x)=0` has

A

(a) atleast one root in (0, 1)

B

(b) atleast one root in (1, 2)

C

(c) atleast one root in `(-1, 0)`

D

(d) data insufficient

Text Solution

Verified by Experts

The correct Answer is:
A
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • DY / DX AS A RATE MEASURER AND TANGENTS, NORMALS

    ARIHANT MATHS|Exercise Exercise (More Than One Correct Option Type Questions)|15 Videos

  • DY / DX AS A RATE MEASURER AND TANGENTS, NORMALS

    ARIHANT MATHS|Exercise Exercise (Statement I And Ii Type Questions)|7 Videos

  • DY / DX AS A RATE MEASURER AND TANGENTS, NORMALS

    ARIHANT MATHS|Exercise Exercise For Session 6|4 Videos

  • DIFFERENTIATION

    ARIHANT MATHS|Exercise Exercise For Session 10|4 Videos

  • ELLIPSE

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|26 Videos

Similar Questions

Explore conceptually related problems

If f(x)=(a-x^(n))^(1//n),"where a "gt 0" and "n in N , then fof (x) is equal to

Let f(x)=x^(3)+ax^(2)+bx+c be the given cubic polynomial and f(x)=0 be the corresponding cubic equation, where a, b, c in R. Now, f'(x)=3x^(2)+2ax+b Let D=4a^(2)-12b=4(a^(2)-3b) be the discriminant of the equation f'(x)=0 . If D=4(a^(2)-3b)gt0 and f(x_(1)).f(x_(2))=0" where " x_(1),x_(2) are the roots of f(x) , then

Let f(x)=x^(3)+ax^(2)+bx+c be the given cubic polynomial and f(x)=0 be the corresponding cubic equation, where a, b, c in R. Now, f'(x)=3x^(2)+2ax+b Let D=4a^(2)-12b=4(a^(2)-3b) be the discriminant of the equation f'(x)=0 . If D=4(a^(2)-3b)gt0 and f(x_(1)).f(x_(2))gt0 where x_(1),x_(2) are the roots of f(x), then

The probability that the roots of the equation x^(2)+nx +(n+1)/2 are real where n in N (N set of natural numbers ) and n le 5 is :

Let f(x)=x^(3)+ax^(2)+bx+c be the given cubic polynomial and f(x)=0 be the corresponding cubic equation, where a, b, c in R. Now, f'(x)=3x^(2)+2ax+b Let D=4a^(2)-12b=4(a^(2)-3b) be the discriminant of the equation f'(x)=0 . IF D=4(a^(2)-3b)lt0 . Then, a. f(x) has all real roots b. f(x) has one real and two imaginary roots c. f(x) has repeated roots d. None of the above

Let f(x)=x^(3)+ax^(2)+bx+c be the given cubic polynomial and f(x)=0 be the corresponding cubic equation, where a, b, c in R. Now, f'(x)=3x^(2)+2ax+b Let D=4a^(2)-12b=4(a^(2)-3b) be the discriminant of the equation f'(x)=0 . If D=4(a^(2)-3b)gt0 and f(x_(1)).f(x_(2)) lt0" where " x_(1),x_(2) are the roots of f(x), then a. f(x) has all real and distinct roots b. f(x) has three real roots but one of the roots would be repeated c. f(x) would have just one real root d. None of the above

Prove that the function f(x) = x^(2n) + 1 is continuous at x = n , n > 0

Is the function f(X) = {:{((1-x^n)/(1-x), x ne 1),(n-1,x=1):} , n in N continuous at x =1?

Let n in N , if the value of c prescribed in Roole's theorem for the function f(x)=2x(x-3)^(n) on [0, 3]" is "(3)/(4) , then n is equat to

Let f(x) be a periodic function with period 3 and f(-2/3)=7 and g(x) =int_0^x f(t+n) dt .where n=3k, k in N . Then g'(7/3) =

Home
Profile