Review question

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?