Home
Class 12
MATHS
In the quadratic equation ax^2 + bx + c ...

In the quadratic equation `ax^2 + bx + c = 0`. if `delta = b^2-4ac` and `alpha+beta , alpha^2+beta^2 , alpha^3+beta^3` and `alpha,beta` are the roots of `ax^2 + bx + c =0`

A

`Delta!=0`

B

`bDelta=0`

C

`cb!=0`

D

`cDelta=0`

Text Solution

Verified by Experts

The correct Answer is:
D

`(alpha^(2)+beta^(2))=(alpha+beta)(alpha^(3)+beta^(3))`
`implies{(alpha+beta)^(2)-2alpha beta}^(2)=(alpha+beta){(alpha+beta)^(2)-2alpha beta(alpha +beta)}`
`=((b^(2))/(a^(2))-(2c)/a)^(2)=(-b/a)((-b^(3))/(a^(3))+(3bc)/(a^(2)))`
`implies((b^(2)-2ac)/(a^(2)))^(2)=((-b)/a)((-b^(3)+3abc)/(a^(3)))`
`implies4a^(2)c^(2)=acb^(2)`
`impliesac(b^(2)-4ac)=0`
As `a!=0`
`impliesc Delta=0`
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • THEORY OF EQUATIONS

    ARIHANT MATHS|Exercise Exercise (Subjective Type Questions)|24 Videos
  • THE STRAIGHT LINES

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|18 Videos
  • THREE DIMENSIONAL COORDINATE SYSTEM

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|44 Videos

Similar Questions

Explore conceptually related problems

In the quadratic equation ax^(2)+bx+c=0, if fDelta=b^(2)-4ac and alpha+beta,alpha^(2)+beta^(2),alpha^(3)+beta^(3) are in GP.where alpha,beta are the roots of ax^(2)+bx+c=0, then

In the quadratic ax^(2)+bx+c=0,D=b^(2)-4ac and alpha+beta,alpha^(2)+beta^(2),alpha^(3)+beta^(3) are in G.P,where alpha,beta are the roots of ax^(2)+bx+c, then (a) Delta!=0( b) b Delta=0 (c) cDelta =0(d) Delta =0'

Knowledge Check

  • Let f(x) = ax^(2) + bx + c, a != 0 and Delta = b^(2) - 4ac . If alpha + beta, alpha^(2) + beta^(2) and alpha^(3) + beta^(3) are in GP, then

    A
    `Dleta != 0`
    B
    `b Delta = 0`
    C
    `c Delta = 0`
    D
    `bc != 0`
  • If alpha, beta are the roots of ax^(2) +bx+c=0 and alpha + beta, alpha^(2)+beta^(2) alpha^(3)+beta^(3) are in G.P., then

    A
    `Delta ne 0`
    B
    `b Delta =0`
    C
    `cb ne 0`
    D
    `c Delta =0`
  • If alpha, beta are roots of ax^(2) -2bx +c=0 , then alpha^(3) beta^(3) + alpha^(2) beta^(3) +alpha^(3) beta^(2) is

    A
    `(c^(2)(c+2ab))/(a^(3))`
    B
    `(bc^(3))/(a^(3))`
    C
    `(c^(2))/(a^(3))`
    D
    `none
  • Similar Questions

    Explore conceptually related problems

    If alpha,beta are the roots of the quadratic equation ax^(2)+bx+c=0 then alpha beta =

    Let alpha,beta be the roots of the quadratic equation ax^(2)+bx+c=0and=b^(2)-4a*If alpha+beta,alpha^(2)+beta^(2)alpha^(3)+beta^(3) are in G.P.Then a.=0 b.!=0 c.b=0 d.c=0

    If alpha and beta are the roots of equation ax^2 + bx + c = 0, then the value of alpha/beta + beta/alpha is

    If the roots of a quadratic equation ax^(2)+ bx +c = 0 are alpha and beta then the quadratic equation having roots alpha^(2) and beta^(2) is :

    If alpha beta( alpha lt beta) are two distinct roots of the equation. ax^(2)+bx+c=0 , then