The roots of the equation `px^(2) - 2(p + 2) x + 3p = 0` differ by 2 Find p and also the roots.

If the roots of the equation x^(3) - px^(2) + qx - r = 0 are in A.P., then

If the roots of the equation x^(2)+5x-p=0 differ by unity, then the value of p is

If alpha,beta are the roots of the equation x^(2) + Px + P^(3) = 0, P ne 0 such that alpha =beta^(2) then the roots of the given equation are

Find the values of p for which both the roots of the equation 4x^2 - 20px + (25p^2 + 15p - 66) = 0 are less than 2.

If the roots of the equation x^(3) - px^(2) + qx - r = 0 are in A.P., then prove that, 2p^3 −9pq+27r=0

If p + iq be one of the roots of the equation x^(3) +ax +b=0 ,then 2p is one of the roots of the equation

The roots of the equation px^(2)-2(p+1)x+3p=0 are alpha and beta . If alpha-beta=2 , calculate the value of alpha,beta and p.

If the roots of the equation px ^(2) +qx + r=0, where 2p , q, 2r are in G.P, are of the form alpha ^(2), 4 alpha-4. Then the value of 2p + 4q+7r is :

Let a and p be the roots of equation x^2 + x - 3 = 0 . Find the value of the expression 4p^2 - a^3 .

If the roots of the equation qx^(2)+2px+2q=0 are real and unequal, prove that the roots of the equation (p+q)x^(2)+2qx+(p-q)=0 are imaginary.