26quad x^(2)-32 gamma+105

if alpha,beta,gamma are non-constant terms in G.P.and equations alpha x^(2)+2 beta x+gamma=0 and x^(2)+x-1=0 has a common root then (gamma-alpha)*beta is

The equation x^2+2(gamma+1)x+a(a-4)=0 has negative roots only if gamma belongs to the interval _________ .

x^2-32x-105

If the centroid of the tetrahedron O-ABC, where A-=(alpha,5,6), B-=(1,beta,4) and C-=(3,2,gamma) is G(1,-1,2) , then: alpha^(2) + beta^(2) + gamma^(2)=

If alpha, beta, gamma are the roots of the equation x^(3) - 6x^(2) + 11x - 6 = 0 and if a = alpha^(2) + beta^(2) + gamma^(2) , b = alpha beta + beta gamma + gamma alpha and c = (alpha + beta) (beta + gamma)(gamma + alpha), then the correct inequality among the following is :

If alpha, beta, gamma are roots of x^(3) - 2x^(2) + 3x - 4 = 0 , then the value of alpha^(2) beta^(2) + beta^(2) gamma^(2) + gamma^(2) alpha^(2) 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 -

Percentage of free space in cubic close-packed structure and in body-centred packed structure are, respectively, (1) 48% and 26% (2) 30% and 26% (3) 26% and 32% (4) 32% and 48%

If alpha , beta , gamma are the roots of x^3 + 4x +1 =0 then the equation whose roots are ( alpha^2)/( beta + gamma ) , ( beta^2)/( gamma + alpha) , ( gamma^2)/ ( alpha + beta) is