Home
Class 12
MATHS
Find the value of k if x^3=3x+a=0 has th...

Find the value of `k` if `x^3=3x+a=0` has three real distinct roots.

A

`a gt 2`

B

`a lt 2`

C

`-2 lt a lt 2`

D

none

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • MAXIMA AND MINIMA

    MOTION|Exercise EXERCISE -1 (SECTION- F )|2 Videos

  • MAXIMA AND MINIMA

    MOTION|Exercise EXERCISE -2 (LEVEL- I)|26 Videos

  • MAXIMA AND MINIMA

    MOTION|Exercise EXERCISE -1 (SECTION - D )|3 Videos

  • MATRICES

    MOTION|Exercise Exercise - 4 (Level-II)|28 Videos

  • METHOD OF DIFFERENTIATION

    MOTION|Exercise EXERCISE - 4 LEVEL -II|5 Videos

Similar Questions

Explore conceptually related problems

Find the value of a if x^(3)-3x+a=0 has three distinct real roots.

Draw the graph of y = xe^(x) .Also (i) Find the range of the functionf (ii) Find the point of inflection. (iii)Find the values of k if 1xe^(x) =k has two distinct real roots

If the equation 2x^(3) -6x + k=0 has three real and distinct roots, then find the value (s) of k.

Let f(x)=x^(3)-3x^(2)+[a]. If a in[alpha,beta) be the complete range of values of 'a' for whichf(x)=0has three real and distinct solutions.then (beta-alpha) is equal to

The equation x^(3) - 3x + [a] = 0 , will have three real and distinct roots if (where [*] denotes the greatest integer function)

If f(x) is a real valued polynomial and f (x) = 0 has real and distinct roots, show that the (f'(x)^(2)-f(x)f''(x))=0 can not have real roots.

If the function f(x) = x^3-9x^2 +24x + c has three real and distinct roots alpha,beta and gamma, then the value of [alpha]+[beta]+[gamma] is

Find value of k if equation x^(3)-3x^(2)+2=k has i 3 real roots ii) 1 real root

The value of k so that the equation x^(3)-12x+k=0 has distinct roots in [0,2] is

Let f(x)=ax^(3)+bx^(2)+cx+d,a!=0 If x_(1) and x_(2) are the real and distinct roots of f'(x)=0 then f(x)=0 will have three real and distinct roots if