Home
Class 12
MATHS
Let x1, x2, x3 be the roots of equation ...

Let `x_1, x_2, x_3` be the roots of equation `x^3-x^2+beta x+gamma=0`. If , `x_1,x_2,x_3` are in A.P. then

A

`beta in (-prop,(1)/(3)]`

B

`beta in [(1)/(3),prop)`

C

`gamma in (-prop,-(1)/(27)]`

D

`gamma in [-(1)/(27),prop)`

Text Solution

Verified by Experts

The correct Answer is:
A, D
Promotional Banner

Topper's Solved these Questions

  • SEQUENCE & SERIES

    MOTION|Exercise Exercise -3 Subjective /JEE Advanced|35 Videos

  • SEQUENCE & SERIES

    MOTION|Exercise Exercise -3 Subjective /JEE Advanced (Comprehension )|3 Videos

  • SEQUENCE & SERIES

    MOTION|Exercise Exercise -2 (Level -I) Objective Problems /JEE Main AP|23 Videos

  • QUADRATIC EQUATION

    MOTION|Exercise EXERCISE 4 (PREVIOUS YEAR| JEE MAIN)|25 Videos

  • SOLUTION OF TRIANGLE

    MOTION|Exercise EXERCISE - 4( LEVEL II)|10 Videos

Similar Questions

Explore conceptually related problems

Let x_(1),x_(2),x_(3) bet the roots of equation x^(3) - x^(2) +betax + gamma = 0 If x_(1),x_(2),x_(3) are in A. P ., then

Let x_(1),x_(2),x_(3) satisfying the equation x^(3)-x^(2)+beta x+gamma=0 are in GP where (x_(1),x_(2),x_(3)>0), then the maximum value of [beta]+[gamma]+2 is,[.] is greatest integer function.

The real numbers x_(1),x_(2),x_(3) satisfying the equation x^(3)-x^(2)+bx+gamma=0 are in A.P. Find the intervals in which beta and gamma lie.

Let x_1,x_2 be the roots of the equation x^2-3x+A=0 and x_3,x_4 be those of equation x^2-12x+B=0 and x_1,x_2,x_3,x_4 form an increasing G.P. find A and B.

Let alpha, and beta are the roots of the equation x^(2)+x +1 =0 then

Let A(alpha, 1/(alpha)),B(beta,1/(beta)),C(gamma,1/(gamma)) be the vertices of a DeltaABC where alpha, beta are the roots of the equation x^(2)-6p_(1)x+2=0, beta, gamma are the roots of the equation x^(2)-6p_(2)x+3=0 and gamma, alpha are the roots of the equation x^(2)-6p_(3)x+6=0, p_(1),p_(2),p_(3) being positive. Then the coordinates of the cenroid of DeltaABC is

alpha and beta are the roots of the equation x^(2)-3x+a=0 and gamma and delta are the roots of the equation x^(2)-12x+b=0 .If alpha,beta,gamma, and delta form an increasing GP., then (a,b)-

Let alpha,beta,gamma be the roots of the cubic 2x^(3)+9x^(2)-27x-54=0. If alpha,beta,gamma are in GP,then find (2)/(3)(| alpha|+| beta|+| gamma|)