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.

If the equations px^2+2qx+r=0 and px^2+2rx+q=0 have a common root then p+q+4r=

If the equations px^(2)+qx+r=0 and rx^(2)+qx+p=0 have a negative common root then the value of (p-q+r)=

If quadratic equations x^(2)+px+q=0 & 2x^(2)-4x+5=0 have a common root then p+q is never less than {p,q in R}:-

Prove that equations (q-r)x^(2)+(r-p)x+p-q=0 and (r-p)x^(2)+(p-q)x+q-r=0 have a common root.

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 p and q are the roots of the equation x^2 - 15x + r = 0 and. p - q = 1 , then what is the value of r?

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