Suppose that the function f(x) and g(x) satisfy the system of equations `f(x)+3g(x)=x^(2)+x+6`
and `2f(x)+4g(x)=2x^(2)+4` for every x. The value of `x` for which `f(x)=g(x)` can be equal to

Options

A. `-2`
B. `2`
C. `-5`
D. `5`

Answer

A, D

Explanation

`f(x)+3g(x)=x^(2)+x+6` ..(i)
`2f(x)+4g(x)=2x^(2)+4` .(ii)
(i). `X2-(ii)implies2g(x)=2x+8`
`g(x)=x+4`
`impliesf(x)=x^(2)+x+6-3g(x)`
`=x^(2)+x+6-3(x+4)`
`=x^(2)-2x-6`
`f(x)=g(x)impliesx+4=x^(2)-2x-6`
`impliesx^(2)-3x-10=0`
`(x-5)(x+2)=0`
`impliesx-2,5`