Ifalpha,beta are the roots of x^2+px+q=0...

If`alpha,beta` are the roots of `x^2+px+q`=0 and also of `x^(2n)+p^n x^n+q^n=0` and if `alpha/beta,beta/alpha` are root of `x^n+1+(x+1)^n`=0, then n is

an integer

an odd integer

an even integer

none of the above

Text Solution

Verified by Experts

The correct Answer is:

Topper's Solved these Questions

QUADRATIC EQUATION
PATHFINDER|Exercise QUESTION BANK|19 Videos
RECTANGULAR CO-ORDINATES
PATHFINDER|Exercise QUESTION BANK|27 Videos

Similar Questions

Explore conceptually related problems

If alpha,beta are the roots of x^2+p x+q=0a n dx^(2n)+p^n x^n+q^n=0a n di f(alpha//beta),(beta//alpha) are the roots of x^n+1+(x+1)^n=0,t h e nn( in N) a. must be an odd integer b. may be any integer c. must be an even integer d. cannot say anything

If alpha,beta are the roots of x^2-px+1=0 and gamma is a root of x^2+px+1=0 , then (alpha+gamma)(beta+gamma) is

If alpha,beta are the roots x^(2)-px+1=0 and gamma "is a root of "x^(2)+px+1=0 ,then (alpha+gamma)(beta+gamma) is -

Let alpha,beta in Rdot If alpha,beta^2 are the roots of quadratic equation x^2-p x+1=0. a n dalpha^2,beta are the roots of quadratic equation x^2-q x+8=0, then find p ,q,alpha,betadot

If alpha, beta are the roots of x^(2) - px + q = 0 and alpha', beta' are the roots of x^(2) - p' x + q' = 0 , then the value of (alpha - alpha')^(2) + (beta -alpha')^(2) + (alpha - beta')^(2) + (beta - beta')^(2) is

If alpha,beta be the roots of x^2-a(x-1)+b =0,then the value of 1/(alpha^2-aalpha)+1/(beta^2-abeta)+2/(a+b) is

IF alpha,beta be the roots of the equation x^2+px+q=0 , show that 1/(alpha+beta) and 1/alpha+1/beta are the roots of pqx^2+(p^2+q)x+p=0

Let alpha,beta are the roots of x^2+b x+1=0. Then find the equation whose roots are (alpha+1//beta)a n d(beta+1//alpha) .

Let alpha , beta be the roots of x^2-x+p=0 and gamma,delta be the roots of x^2-4x+q=0 . If alpha,beta,gamma are in GP , then the integer values of p and q respectively are:

If alpha and beta are the roots of x^2-x+1=0 ,then the value of alpha^(2013)+beta^(2013) is equal to

PATHFINDER-QUADRATIC EQUATION AND EXPRESSION-QUESTION BANK

If blt0, then the roots x1 and x2 of the equation 2x^2+6x+b=0, satisfy...
Text Solution
|
If (2x^2-3x+1)(2x^2+5x+1)=9x^2,then equation has
Text Solution
|
Ifalpha,beta are the roots of x^2+px+q=0 and also of x^(2n)+p^n x^n+q^...
Text Solution
|
If 3^x.8^(x/(x+2))=6, then x equals.
Text Solution
|
Value (s) of 'a' for which ax^2+(a-3)x+1lt0 for at least one positive ...
Text Solution
|
Number of solution of abs(x^2+4x+3) + 2x+5=0 is/are
Text Solution
|
If roots of x^2-(a-3)x+a=0 are such that both of them is greater than ...
Text Solution
|
solve the inequality(16)^(1//x)/((2^(x+3)))gt1
Text Solution
|
Let alpha,beta be the roots of the equation (x-a)(x-b)=c, c≠ 0. Then t...
Text Solution
|
If p and q are odd integers,then the equation x^2+2px+2q=0
Text Solution
|
If x^2+mx+1=0 and (b-c)x^2+(c-a)x+(a-b)=0 have both roots common,then
Text Solution
|
Solution set of x satisfying abs(x-1)+abs(x-2)+abs(x-3)ge6 is
Text Solution
|
The equation (x/(x+1))^2+(x/(x-1))^2=a(a-1) has
Text Solution
|
If alpha and beta are roots of the equation ax^2+bx+c=0 and, if px^2+q...
Text Solution
|
Ifax^2-bx+c=0 has two distinct roots lying in the interval (0,1),a,b,c...
Text Solution
|
If ax^2+bx+c=0 and cx^2+bx+a=0 (a,b,cinR) have a common non-real roots...
Text Solution
|
LetP(x)=0 be the polynomial equation of least possible degree with rat...
Text Solution
|
If 2a+3b+6c=0(a,b,cinR), then the quadratic equation ax^2+bx+c=0 has
Text Solution
|
If (alpha,beta)∈ R are two of an quadratic equations,then the equation...
Text Solution
|
If a,binR are two of an quadratic equations,then the equation will be ...
Text Solution
|