If the equations `x^3+x^2-4x=4 and x^2+p x+2p=0 (p in R)`have two roots common, then the value of p is

If the equations x^(3)+x^(2)-4x=4 and x^(2)+px+2p=0(p in R) have two roots common,then the value of p is

If x^(2)-3x+2=0,3x^(2)+px+q=0 have two roots common then the value of p and q is

If the equations x^(3)+5x^(2)+px+q=0 and x^(3)+7x^(2)+px+r=0 (a,q,r in R) have exactly two roots common,then p:q:r is

If the equations x^(2)-x-p=0 and x^(2)+2px-12=0 have a common root,then that root is

If x^(2)-8x+15=0 and (x-2)(x-p)=0 and one root is common then p is

If the equation x^2 + px + q =0 and x^2 + p' x + q' =0 have common roots, show that it must be equal to (pq' - p'q)/(q-q') or (q-q')/(p'-p) .

If p, q, r are in G.P. and the equations, p x^2+2q x+r=0 and dx^2+2e x+f=0 have a common root, then show that d/p ,e/q ,f/r are in A.P.