The equation \(x^2+ax+b=0\), where \(a\) and \(b\) are different, has solutions \(x=a\) and \(x=b\). How many such equations are there?

Here the blue curve is \(y = x^2 + ax+b\), while the red curve is \(y = (x-a)(x-b)\).

Can you adjust \(a\) and \(b\) so that the roots of the two curves are the same?

In this case, what can we say about the two curves?