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 equations 2x^(2)-7x+1=0 and ax^(2)+bx+2=0 have a common root, then

The value of b for which the equation x^2+bx-1=0 and x^2+x+b=0 have one root in common is

The equations x^(2)-6X+a=0 and x^(2)-bx+6=0 have one root in common. The other root of the first one and the second equation are integers in the ratio 4 : 3 . Find the commonroot.

The quadratic equations x^(2)-6x+a=0" and "x^(2)-cx+6=0 have one root in common. The other roots of the first and second equations are integers in the ratio 4 : 3. Then the common root is

The equations x^(2) - 4x +a=0 and x^(2) + bx +5=0 have one root in common The other root of these equations are integers in the ratio 3 : 5Find the common root

If the equation x^2-ax+a+2=0 has equal roots then 'a' will be :

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 the equation x^2-3p x+2q=0a n dx^2-3a x+2b=0 have a common roots and the other roots of the second equation is the reciprocal of the other roots of the first, then (2-2b)^2 . a. 36p a(q-b)^2 b. 18p a(q-b)^2 c. 36b q(p-a)^2 d. 18b q(p-a)^2

If the equation x^(3)+k x^(2)+3=0 and x^(2)+k x+3=0 have a common root, then the value k .