Question

If x^2 - 11x + a = 0 and x^2 - 14x + 2a = 0 have one common root then a= ?

Answer 1

x2 - 11x + a = 0...i

=> a = 11x - x2

Similarly,

2a = 14x - x2

=> a = (14x - x2)/2...ii

Equating i and ii

11x - x2 = (14x - x2)/2

=> 22x - 2x2 = 14x - x2

=> x2 - 8x = 0

=> x(x - 8) = 0

=> x=0 or x=8

Therefore

a = 11(0) - (0)^2 = 0

OR

a = 11(8) - (8)^2 = 88 - 64 = 22