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 a ,b ,a n dc are in G.P., then the equations a x^2+2b x+c=0a n ddx^2+2e x+f=0 have a common root if d/c , e/b ,f/c are in a. A.P. b. G.P. c. H.P. d. none of these

a ,b ,c are positive real numbers forming a G.P. If ax^2+2b x+c=0 and dx^2+2e x+f=0 have a common root, then prove that d//a ,e//b ,f//c are in A.P.

a ,b ,c are positive real numbers forming a G.P. ILf a x^2+2b x+c=0a n ddx^2+2e x+f=0 have a common root, then prove that d//a ,e//b ,f//c are in A.P.

If p(q-r)x^(2) + q(r-p)x+ r(p-q) = 0 has equal roots, then show that p, q, r are in H.P.

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 x^(2)+px+q=0 and x^(2)+qx+p=0 have a common root, prove that either p=q or 1+p+q=0 .

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.