Home
Class 12
MATHS
Let alpha and beta be the roots of equat...

Let `alpha and beta` be the roots of equation `px^2 + qx + r = 0 , p != 0`.If `p,q,r` are in A.P. and `1/alpha+1/beta=4`, then the value of `|alpha-beta|` is :

A

`(sqrt(34))/(9)`

B

`(2sqrt(13))/(9)`

C

`(sqrt(61))/(9)`

D

`(2sqrt(17))/(9)`

Text Solution

Verified by Experts

Since `alpha and beta` are roots of the the equation `px^(2)+qx+r=0`. Therefore, `alpha+beta = - (q)/(p) and alpha beta = (r)/(p)`
Now, `(1)/(alpha)+(1)/(beta)=4 rArr (alpha+beta)/(alpha beta)=4 rArr -(q)/(r)=4 rArr q =-4r`
It is given that p,q, r are in AP. Therefore, `2q = p+r rArr -8r = p+r rArr p = -9r`
`therefore" "alpha + beta = -(q)/(p) = -(4)/(9) and alpha beta =(r)/(p) = -(1)/(9)`
Now, `(alpha - beta)^(2) = (alpha+beta)^(2) - 4 alpha beta`
`rArr" "(alpha-beta)^(2)=(16)/(81)+(4)/(9)=(52)/(81) rArr |alpha-beta|=(2 sqrt(13))/(9)`
Promotional Banner

Similar Questions

Explore conceptually related problems

Let alpha and beta be the roots of equation px^2 +qx+r =0 , p ne 0, if p,q, r are in A.P and (1)/ alpha +(1)/( beta ) =4 then the value of | alpha - beta | is

Let alpha and beta be the roots of equation px^(2) + qx + r = 0, p ne 0 . If p, q , r are in A.P. and (1)/(alpha) + (1)/(beta) = 4, then the value of | alpha - beta| is :

Let alpha and beta be the roots of equation px^(2)+qx+r=0,p!=0 .If p, q ,r are in A.P. and ((1)/(alpha)+(1)/(beta))= 4 , then the value of | alpha -beta|

Let alpha and beta be the roots of equation px^(2) + qx + r = 0 , p ne 0 . If p , q, r are in A.P . And (1)/(alpha ) + (1)/(beta) = 4 , then the value of |alpha - beta| is

Let alpha and beta be the roots of equation px^(2)+qx+r=0" " pne0."If " p , q , r "are in A.P" and (1)/(alpha)+(1)/(beta)=4 , "then the value of " |alpha-beta| is -

Let alpha and beta the roots of equation px^(2) + qx + =0 p ne 0 if p,q,r are in A.P and (1)/(alpha) + (1)/(beta) =4 then the value of |alpha -beta| is :

Let alpha and beta be the roots of equation px^(2)+qx+r=0,p!=0. If p,q,r are in A.P and (1)/(alpha)+(1)/(beta)=4 then the value of | alpha-beta| is (a) (sqrt(34))/(9) (b) (2sqrt(13))/(9) (c) (sqrt(16))/(9) (d) (2sqrt(17))/(9)

Let alpha and beta be the roots of equation px^2+qx+r=0,pne0 . If p, q, r are in A.P. and 1/alpha+1/beta =4, then the value of abs(alpha-beta) is :