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^(3) + 5x^(2) + px + q = 0 and x^(3) + 7x^(2) + px + r = 0 have two roots in common, then the product of two non-common roots of two equations, is

Let the equations x^(3)+2x^(2)+px+q=0and x^(3)+x^(2)+px+r=0 have two toots in common and the third root of each equation are represented by alphaand beta respectively, find the value of |alpha+beta|

if the equation x^(2)+qx+rp=0 and x^(2)+rx+pq=0,(q!=r) have only one root in common, then prove that p+q+r=0 .

If the equadratic equation 4x ^(2) -2x -m =0 and 4p (q-r) x ^(2) -2p (r-p) x+r (p-q)-=0 have a common root such that second equation has equal roots then the vlaue of m will be :

If the equadratic equation 4x ^(2) -2x -m =0 and 4p (q-r) x ^(2) -2p (r-p) x+r (p-q)-=0 have a common root such that second equation has equal roots then the vlaue of m will be :

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

If the quadratic equations x^(2) +pqx +r=0 and z^(2) +prx +q=0 have a common root then the equation containing their other roots is/are

x^(3)+5x^(2)+px+q=0 and x^(3)+7x^(2)+px+r=0 have two roos in common. If their third roots are gamma_(1) and gamma_(2) , respectively, then |gamma_(1)+gamma_(2)|=

If -4 is a root of the equation x^(2)+px-4=0 and the equation x^(2)+px+q=0 has equal roots, then the value of q is

The equation x^3+px^2+qx+r=0 and x^3+p\'x^2+q\'x+r'=0 have two common roots, find the quadratic whose roots are these two common roots.