Question

Two distinct polynomial f(x) and g(x) are defined as follows: f (x) = x^2 +ax + 2 ; g(x) =x^2 + 2 x +a .If the equation f (x) = 0 and g(x) = 0 have a common root then the sum of the roots of the equation f (x) + g(x) = 0 is (A) -1/2 (B) 0 (C) 1/2 (D) 1 .

Answer 1

Given f(x)=g(x) x^2+ax+2=x^2+2x+a ax+2=2x+a ax-2x=a-2 x(a-2)=a-2 x=(a-2)/(a-2) x=1 Answer isD

Answer 2

x^2 + ax + 2 = 0

x^2 + 2x + a = 0

Equating these equations we get x = 1

Putting in any of the above equations we get a = -3

Add the original equations

2x^2 + (2+a)x + (2+a) = 0

Putting a = -3 we get

2x^2 - x - 1 = 0

Solving this equation we get the roots 1 and -1/2

Which gives sum of roots = 1 + (-1/2) = 1/2

Therefore (C) 1/2 is the correct answer