Question 9
Suppose that $b$ and $c$ are real numbers such that the equation
$$
x^{2}+b x+c=0
$$
has two different solutions $x_{1}, x_{2}$. Suppose that
a. The (positive) difference between $x_{1}$ and $x_{2}$ is $1$;
b. The (positive) difference between $b$ and $c$ is also $1$.
Find all possible values of $b$ and $c$.
$$
x^{2}+b x+c=0
$$
has two different solutions $x_{1}, x_{2}$. Suppose that
a. The (positive) difference between $x_{1}$ and $x_{2}$ is $1$;
b. The (positive) difference between $b$ and $c$ is also $1$.
Find all possible values of $b$ and $c$.