Question

If `f(x) = x^2-2x` and `g(x) = 6x+4`, for which value of `x` does `(f+g)(x)=0`?

Answer 1

`x=-2`

Explanation:

`(f+g)(x)=f(x)+g(x)`

`rArrf(x)+g(x)`

`=x^2-2x+6x+4`

`=x^2+4x+4`

`"to solve "x^2+4x+4=0`

`"factorise by grouping"`

`x^2+2x+2x+4=0larr" split the x-term"`

`color(red)(x)(x+2)color(red)(+2)(x+2)=0`

`"factor out "(x+2)`

`(x+2)(color(red)(x+2))=0`

`rArr(x+2)^2=0`

`rArrx=-2" with multiplicity 2"`