The Mathematical Tripos

["Luis Lopes" <llopes@xxxxxxxxxxxxx>]

Problema 3) Obtain the condition, if a, b, and c are real, for the quadratic
equation
ax^2 + 2bx + c = 0 to have real unequal roots.

The numbers alpha, beta, gamma are not equal to -1 or +1, and are such that
alpha^2 + beta^2 + gamma^2 + 2.alpha.beta.gamma = 1.

Prove that if alpha, beta, gamma are real then either all three lie
between -1 and +1 or all three lie outside this range.

Source: Problem 1) Math. Tripos 1952  Part 1, Paper IV.

[ ]'s
Lu'is