Let alpha,beta be the roots of the equa...

Let `alpha,beta` be the roots of the equation `x^(2)-px+r=0` and `(alpha)/(2),2beta` be the roots of the equation `x^(2)-qx+r=0` then the value of r is

`(2)/(9)(p-q)(2 q-not p)`

`(2)/(9)(q-p)(2 p-q)`

`(2)/(9)(q-2 p)(2 q-p)`

`(2)/(9)(2 p-2 q)(2 q-p)`

Text Solution

Verified by Experts

The correct Answer is:

Topper's Solved these Questions

PROGRESSIONS
HIMALAYA PUBLICATION|Exercise QUESTION BANK|97 Videos
SETS,RELATIONS AND FUNCTIONS
HIMALAYA PUBLICATION|Exercise QUESTION BANK|285 Videos

Similar Questions

Explore conceptually related problems

Let alpha, beta be the roots of the equation x^(2) - px + r = 0 and (alpha)/(2) , 2 beta be the roots of the equation x^(2) - qx + r = 0 . Then the value of r is :

If alpha,beta are roots of the equation 6x^(2) + 11x + 3 = 0 then :

If alpha and beta are the root of the equation x^(2)-x+1=0 then alpha^(2009)+beta^(2009)=

If alpha, beta are the roots of the equation x^(2)-2x-a^(2)+1=0 and gamma, delta are the roots of the equation x^(2)-2(a+1)x+a(a-1)=0 such that alpha, beta epsilonn (gamma, delta) find the value of a .

Let alpha and beta be roots of the equation X^(2)-2x+A=0 and let gamma and delta be the roots of the equation X^(2)-18x+B=0 . If alpha lt beta lt gamma lt delta are in arithmetic progression then find the valus of A and B.

Let a ,b , c ,p ,q be real numbers. Suppose alpha,beta are the roots of the equation x^2+2p x+q=0,alphaa n d1//beta are the roots of the equation a x^2+2b x+c=0,w h e r ebeta^2 !in {-1,0,1}dot Statement 1: (p^2-q)(b^2-a c)geq0 Statement 2: b!=p aorc!=q a

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

If alpha, beta are the rots of a x^(2)+b x+c=0 and alpha+h, beta+h are the roots of p x^(2)+q x+r=0 then h=

Let alpha, beta the roots of the equation (x - a) (x - b) = c , c ne 0. Then the roots of the equation (x - alpha ) x - beta) + c = 0 are :

If alpha, beta are the roots of x^(2)-a x+b=0 and A_(n)='alpha'^(n)+beta^(n) , then A_(n+1)=

HIMALAYA PUBLICATION-QUADRATIC EQUATIONS AND EXPRESSION-Question Bank

Let a,b,c be the sides of a triangle no two of them are equal and la...
Text Solution
|
If alpha, beta are the roots of the equation x^(2)+x+1=0, then the equ...
Text Solution
|
Let alpha,beta be the roots of the equation x^(2)-px+r=0 and (alpha)/...
Text Solution
|
The smallest value of k for which both the roots of the equation x^(2)...
Text Solution
|
The minimum positive value of (x^(2)+2 x+4)/(x+2) is
Text Solution
|
Let p and q be real number such that p ne 0 , p^(3) ne q and p^(3...
Text Solution
|
If p and q are the roots of the equation x^(2)+p x+q=0 then
Text Solution
|
If the difference between the roots of x^(2)+a x+b=0 is same as that o...
Text Solution
|
If alpha ne beta and alpha^(2) = 5 alpha - 3, beta^(2) = 5 beta - 3 , ...
Text Solution
|
The number of real roots of the equation |x|^(2)-3|x|+2=0 is
Text Solution
|
If one root of the equation x^(2)+p x+12=0 is 4, while the equation x^...
Text Solution
|
If 2 a+3 b+6 c=0, a, b, c in R then the equation a x^(2)+b x+c=0 has a...
Text Solution
|
If (1-p) is a root of the quadratic equation x^(2)+p x+(1-p)=0 then it...
Text Solution
|
The value of a for which the sum of the squares of the roots of the eq...
Text Solution
|
If both the roots of the quadratic equation x^(2)-2 k x+(k^(2)+k-5)=0 ...
Text Solution
|
If x is real, the maximum value of (3 x^(2)+9 x+17)/(3 x^(2)+9 x+7) is
Text Solution
|
All the values of m for which both roots of the equation x^(2)-2 m x+(...
Text Solution
|
If the roots of the quadratic equation x^(2)+p x+q=0 are tan 30^(circ)...
Text Solution
|
If the difference between the roots of the equation x^(2)+a x+1=0 is l...
Text Solution
|
The quadratic equations : x^(2) - 6x + a = 0 and x^(2) - cx + 6 = ...
Text Solution
|