Find the number of ordered pairs $(a,b)$ of real numbers such that

$\bullet$ $a$ is a root of $x^2 + ax + b = 0,$ and

$\bullet$ $b$ is a root of $x^2 + ax + b = 0.$
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Find the number of ordered pairs $(a,b)$ of real numbers such that

$\bullet$ $a$ is a root of $x^2 + ax + b = 0,$ and

$\bullet$ $b$ is a root of $x^2 + ax + b = 0.$
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
3
Find the number of ordered pairs $(a,b)$ of real numbers such that

$\bullet$ $a$ is a root of $x^2 + ax + b = 0,$ and

$\bullet$ $b$ is a root of $x^2 + ax + b = 0.$
train