If the equations `ax^(2) +2bx +c = 0 and Ax^(2) +2Bx+C=0` have a common root and a,b,c are in G.P prove that `a/A , b/B, c/C ` are in H.P

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 ax^(2)+2bx+c=0 and ax62+2cx+b=0b!=c have a common root,then (a)/(b+c)=

If a, b, c are in G.P. and the equation ax^(2) + 2bx + c = 0 and dx^(2) + 2ex + f = 0 have a common root, then show that (d)/(a), (e)/(b), (f)/(c ) are in A.P.

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

If a,b,c are in G.P.L, then the equations ax^(2) + 2bx + c = 0 0 and dx^(2) + 2ex+ f = 0 have a common root if ( d)/( a) , ( e )/( b ) , ( f )/( c ) are in :

If the equations ax^2 + bx + c = 0 and x^3 + x - 2 = 0 have two common roots then show that 2a = 2b = c .

If a, b, c are in G.P then prove that 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 A.P.

If the equations : x^(2) + 2x + 3 = 0 and ax^(2) + bx + c =0 a, b,c in R, Have a common root, then a: b : c is :

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