1.Find the roots of the equation `x^(2)+x-p(p+1)=0`

The set of values of p for which the roots of the equation 3x^(2)+2x+p(p-1)=0 are of opposite signs is :

The set of values of p for which the roots of the equation 3x^(2)+2x+p(p-1)=0 are of opposite signs is:

Let A(alpha, 1/(alpha)),B(beta,1/(beta)),C(gamma,1/(gamma)) be the vertices of a DeltaABC where alpha, beta are the roots of the equation x^(2)-6p_(1)x+2=0, beta, gamma are the roots of the equation x^(2)-6p_(2)x+3=0 and gamma, alpha are the roots of the equation x^(2)-6p_(3)x+6=0, p_(1),p_(2),p_(3) being positive. Then the coordinates of the cenroid of DeltaABC is

Let p be an integer such that both roots of the equation 5x^(2)-5px+(66p-1)=0 are positive integers.Find the value of p

If alpha,beta are the roots of the equation x^(2)-p(x+1)-c=0, then (alpha+1)(beta+1)=

If -2 is a root of the equation 3x^(2)+7x+p=0, find the value of k so that the roots of the equation x^(2)+k(4x+k-1)+p=0 are equal.

If the range of the values of a for which the roots of the equation x ^(2) -2x - a ^(2) +1=0 lie between the roots of the equation x ^(2) -2 (a+1)x +a(a -1) =0 is (p,q), then find the value of (q- (1)/(p)).

If the equation ax^(2)+2bx+c=0 and x^(2)+2p^(2)x+1=0 have one common root and a,b,c are in AP(p^(2)!=1), then the roots of the equation x^(2)+2p^(2)x+1=0 are