Home
Class 12
MATHS
Let alpha,beta,gamma be the roots of (x-...

Let `alpha,beta,gamma` be the roots of `(x-a) (x-b) (x-c) = d, d != 0`, then the roots of the equation `(x-alpha)(x-beta)(x-gamma) + d =0` are `:`

A

a,b,d

B

b,c,d

C

a,b,c

D

`a+d,b+d,c+d`

Text Solution

Verified by Experts

The correct Answer is:
C
Since `alpha, beta` and `gamma` are the roots of
`(x-a)(x-b)(x-c)=d`
`implies(x-a)(x-b)(x-c)-d(x-alpha)(x-beta)(x-gamma)`
`implies(x-alpha)(x-beta)(x-gamma)+d=(x-a)(x-b)(x-c)`
`impliesa,b`and `c` are the roots of
`(x-alpha)(x-beta)(x-gamma)+d=0`
Promotional Banner

Similar Questions

Explore conceptually related problems

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

If alpha,beta are the roots of the equation a x^2+b x+c=0, then find the roots of the equation a x^2-b x(x-1)+c(x-1)^2=0 in term of alpha and beta .

Let alpha,beta be the roots of the equation x^2-p x+r=0 and alpha/2,2beta be the roots of the equation x^2-q x+r=0 , the value of r is

If alpha, beta be the roots of the equation x^2-px+q=0 then find the equation whose roots are q/(p-alpha) and q/(p-beta)

If alpha,beta,gamma are the roots of x^3-x^2-1=0 then the value of (1+alpha)//(1-alpha)+(1+beta)//(1-beta)+(1+gamma)//(1-gamma) is equal to

If alpha,beta,gamma are the roots of x^(3)+2x^(2)-x-3=0 . If the absolute value of the expression (alpha-1)/(alpha+2)+(beta-1)/(beta+2)+(gamma-1)/(gamma+2) can be expressed as (m)/(n) where m and n are co-prime the value of |{:(m,n^(2)),(m-n,m+n):}| is

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 .

If alpha, beta, gamma are the roots of the cubic equation x^(3)+qx+r=0 then the find equation whose roots are (alpha-beta)^(2),(beta-gamma)^(2),(gamma-alpha)^(2) .

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.

If alpha,beta are the roots of x^2+p x+q=0a n dgamma,delta are the roots of x^2+r x+s=0, evaluate (alpha-gamma)(alpha-delta)(beta-gamma)(beta-delta) in lterms of p ,q ,r ,a n dsdot Deduce the condition that the equation has a common root.