If the equation `x^(2)+ax+b=0 and x^(2)+cx+d=0` have a common root and the first equation has equal roots, then prove that `2(b+d)=ac.`

If the equations x^(2)-px+q=0 and x^(2)-ax+b=0 have a common root and the second equation has equal roots then

IF x^2 +bx +a=0, ax^2+x+b=0 have a common root and the first equation has equal roots then 2a^2+b=

IF x^2 +bx +a=0, ax^2+x+b=0 have a common root and the first equation has equal roots then 2a^2+b=

If the equations x^(2) - ax + b = 0 and x^(2) + bx - a = 0 have a common root, then

If the equation x^2-cx+d=0 and x^2-ax+b=0 have a common root,and the roots of the second equations are equal ,then prove that 2(b+d)=ac

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).