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Two distinct polynomials f(x) and g(x...

Two distinct polynomials f(x) and g(x) defined as defined as follow :
`f(x) =x^(2) +ax+2,g(x) =x^(2) +2x+a`
if the equations f(x) =0 and g(x) =0 have a common root then the sum of roots of the equation f(x) +g(x) =0 is -

A

`-(1)/(2)`

B

0

C

`(1)/(2)`

D

1

Text Solution

Verified by Experts

The correct Answer is:
C
Let `alpha ` is the common root
So `alpha^(2)+aalpha +2=0`
` alpha^(2) +2alpha +a=0`
`implies (a-2) alpha +2-a=0`
`alpha =1` is common root.
`:' 1^(2) +a+2-a=0=.a=-3.`
`f(X) +g(x) =0`
`implies 2x^(2) +(a+2)x+(a+2)=0`
`implies 2x^(2) -x-1=0`
`implies `Sum of roots `=(1)/(2)` .
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