Question 10
Let $p$ and $q$ be real numbers such that the quadratic equation
$$
x^2 + px + q = 0
$$
has two real solutions $x_1$ and $x_2$.
The following two conditions hold:
(i) The numbers $x_1$ and $x_2$ differ by 1.
(ii) The numbers $p$ and $q$ differ by 1.
Show that $p, q, x_1$ and $x_2$ are integers.
$$
x^2 + px + q = 0
$$
has two real solutions $x_1$ and $x_2$.
The following two conditions hold:
(i) The numbers $x_1$ and $x_2$ differ by 1.
(ii) The numbers $p$ and $q$ differ by 1.
Show that $p, q, x_1$ and $x_2$ are integers.