Quadratic and Linear Function relationship I just stumbled across this problem and would appreciate some help with it, as I'm not getting far with it.
Problem: You are given a quadratic function $f(x)=ax^2+bx+c$
and a linear function $g(x)$.
The two functions intersect at $x=0$ and at also at an $x$ with $g(x)=f(x)=0$ and where $x<0$.
Which of the two could, for some values of $a,b,c$, be an expression for $g(x)$:

*

*$g(x)=bx+c$

*$g(x)=ax+c$
My Progress thus far:
We know that the $y$-intercept must be $c$, because $f(x)$ and $g(x)$ intercept at $x=0$. So that makes perfect sense. However I fail to see how for some values of $a,b,c$  the gradient of $g(x)$ could either be $a$ or $b$.
Any help would greatly be appreciated.

Given f(x)=$ax^2$+bx+c ($a \neq0$),
if g(x)=bx+c for some x=$x_1$<0,
f($x_1$)=${ax_1}^2$+$bx_1$+c (I)
g($x_1$)=b$x_1$+c  (II)
(I)-(II)  ${ax_1}^2$ = 0, a=0 , it is not allowed.
So, this is not the right choice, only option is (2)  g(x)=ax+c.
You can prove that from here.
