If `a,b,c` are in GP, show that the equations `ax^(2)+2bx+c=0` and `dx^(2)+2ex+f=0` have a common root if `a/d,b/e,c/f` are in HP

If a, b, c are in GP , then the equations ax^2 +2bx+c = 0 and dx^2 +2ex+f =0 have a common root if d/a , e/b , f/c are in

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

If d,e,f are G.P. and the two quadratic equations ax^(2)+2bx+c=0anddx^(2)+2ex+f=0 have a common root, then

If the equation ax^2+2bx+c=0 and ax^2+2cx+b=0 b!=c have a common root ,then a/(b+c =

If the equation x^2+2x+3=0 and ax^2+bx+c=0 have a common root then a:b:c is

If the equation ax^(2) + bx + c = 0 and 2x^(2) + 3x + 4 = 0 have a common root, then a : b : c

If a,b,c in R and the equation ax^2+bx+c = 0 and x^2+ x+ 1=0 have a common root, then

If a,b,c, in R and equations ax^(2) + bx + c =0 and x^(2) + 2x + 9 = 0 have a common root then

If the equation x^2+ax+bc=0" and " x^2-bx+ca=0 have a common root, then a+b+c =

If a, b, c are positive real numbers such that the equations ax^(2) + bx + c = 0 and bx^(2) + cx + a = 0 , have a common root, then