2. Let $a$, $b$, and $c$ be three distinct real numbers such that the equations
$$
x^{2}+a x+1=0 \text { and } x^{2}+b x+c=0
$$

have a common real root, and the equations
$$
x^{2}+x+a=0 \text { and } x^{2}+c x+b=0
$$

also have a common real root. Find $a+b+c$.
Prompt: Example 3. Answer: $a+b+c=-3$.



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Prompt: Example 3. Answer: $a+b+c=-3$.
