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

If p,q,r in R and the quadratic equation px^(2)+qx+r=0 has no real root,then

If p,q,r are in A.P. and are positive, the roots of the quadratic equation px^(2) + qx + r = 0 are real for :

If p,q,r are + ve and are in A.P., the roots of quadratic equation px^2 + qx + r = 0 are all real for

Let alpha and beta be the roots of the equation px^(2) + qx + r=0 . If p, q, r in AP and alpha+beta =4 , then alpha beta is equal to

Let alpha, beta are the 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 roots is equal to product of roots, then the complete range of q 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:

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:

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 :