Problem:
Consider the quadratic equation
where a, b, and denote by
,
its roots. Prove that if
is a real number then
or
.
Proof:
Let . Then,
and
.
If , the roots of the equation are
and it is obvious that
is a real number.
If ,, the roots of the equation are
hence, , as claimed.
QED.
More later,
Nalin Pithwa