Home
Class 12
MATHS
If each pair of the three equations x^(2...

If each pair of the three equations `x^(2)+ax+b=0, x^(2)+cx+d=0` and `x^(2)+ex+f=0` has exactly one root in common then show that `(a+c+e)^(2)=4(ac)+ce+ea-b-d-f`

Promotional Banner

Similar Questions

Explore conceptually related problems

if each pair of the equation x^(2)+ax+b=0,x^(2)+bx+c=0 and x^(2)+cx+a=0 has common root,then product of all common root is

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 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

If the equations x^(2) - ax + b = 0 and x^(2) - ex + f = 0 have one root in common and if the second equation has equal roots, then prove that ae = 2 (b + f).

If the quadratic equations ax^(2)+2bx+c=0 and ax^(2)+2cx+b=0, (b ne c) have a common root, then show that a+4b+4c=0

If the equations x^(2)-ax+b=0 and x^(2)-ex+f=0 have one root in common and if the second equation has equal roots then prove that ae=2(b+f).