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$p(x)$ = $(x-3)(x-2)$, &

$q(x)$ = $(x-2)(x-1)$

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

4d_
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  • Can you give an example of what you mean by two quadratic equations having a common root? Do you mean two equations in two variables, or one? – 5xum Jul 29 '19 at 11:54
  • Sorry, I should have mentioned it. I mean, two quadratic equations in one variable. I'm gonna edit my question – 4d_ Jul 29 '19 at 12:01

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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.

5xum
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