Let p, q, r `in` R and `r gt p gt 0`. If the quadratic equation `px^(2) + qx + r = 0` has two complex roots `alpha and beta`, then `|alpha|+|beta|`, is

Let a,b,c in R and a gt 0 . If the quadratic equation ax^(2) +bx +c=0 has two real roots alpha and beta such that alpha gt -1 and beta gt 1 , then show that 1 + |b/a| + c/a gt 0

Let p, q in R . If 2- sqrt3 is a root of the quadratic equation, x^(2)+px+q=0, then

Given the alpha + beta are the roots of the quadratic equation px^(2) + qx + 1 = 0 find the value of alpha^(3)beta^(2) + alpha^(2)beta^(3) .

If alpha and beta are the roots of the quadratic equation px^(2)+qx+1 , Then the value of alphabeta+alpha^(2)beta^(2) is

Let alpha, beta are two real roots of equation x ^(2) + px+ q =0, p ,q, in R, q ne 0. If the quadratic equation g (x) =0 has two roots alpha + (1)/(alpha) , beta + (1)/(beta) such that sum of its roots is equal to product of roots, then number of integral values g can attain is :

The roots alpha and beta of the quadratic equation px^(2) + qx + r = 0 are real and of opposite signs. The roots of alpha(x-beta)^(2) + beta(x-alpha)^(2) = 0 are:

If alpha and beta are the roots of the quadratic equation x^(2) + px + q = 0 , then form the quadratic equation whose roots are alpha + (1)/(beta), beta + (1)/(alpha)

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 :

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 :

If the equations px^2+2qx+r=0 and px^2+2rx+q=0 have a common root then p+q+4r=