Four Roots in Geometric Progression

★ 7/10Geometric Progression Substitution algebra sequences Vieta's Formulas

Problem

Let $a, b \in \mathbb{R}$ . The four real roots of

\left(x^2 - ax + 1\right)\left(x^2 - bx + 1\right) = 0

form a geometric progression with common ratio $q \in \left[\tfrac13, 2\right]$ . Find the range of $ab$ .

Answer

Solution

Difficulty	7/10
Topics	Geometric Progression, Substitution, algebra, sequences, Vieta's Formulas

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