Question 103
The equations
$$
x^2 + a x + 1 = 0 \text{ and } x^2 + b x + c = 0
$$
have a common real root. In addition, the equations
$$
x^2 + x + a = 0 \text{ and } x^2 + c x + b = 0
$$
have a common real root. What values can the sum $a + b + c$ take?
$$
x^2 + a x + 1 = 0 \text{ and } x^2 + b x + c = 0
$$
have a common real root. In addition, the equations
$$
x^2 + x + a = 0 \text{ and } x^2 + c x + b = 0
$$
have a common real root. What values can the sum $a + b + c$ take?