$p(x)$ = $(x-3)(x-2)$, &
$q(x)$ = $(x-2)(x-1)$
Both equations have a common root $x$ = $2$. I was just wondering if there is any geometrical meaning to it.
For example, geometrical meaning of roots (or zeroes) of an equation $f(x)$ = 0 is the $x-coordinates$ of the points where the graph $y$ = $f(x)$ meets the $x-axis$.
Likewise, geometrical meaning of the equation $f(x)$ = $g(x)$ is the $x-coordinates$ of the point of intersection of $y$ = $f(x)$ and $y$ = $g(x)$
So is there a geometrical meaning to two quadratic equations having a common root? I included the two examples just to make it clear what I am trying to understand. I actually gave it a pretty good thought, but couldn't understand if there is indeed a geometrical meaning to it.
Thanks
Best Answer
A quadratic equation is simply an equation $f(x)=0$, where $f$ is a quadratic function. So if you have two quadratic equations, $f(x)$ and $g(x)$, and $f(x)=g(x)=0$, that means that the lines $y=0$, $y=f(x)$ and $y=g(x)$ all meet in one point.