Month: March 2026

Exploring Descartes’ Rule of Signs

We’ve discussed the Rational Root Theorem in the past, but not a theorem that is often taught along with it, namely Descartes’ Rule of Signs, which predicts the numbers of positive and negative zeros (roots) of a polynomial. Both are ascribed to Rene Descartes; both are often taught without proof. Here we’ll introduce the theorem, …

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Completing the Square for Quadratic Equations

A recent question reminded me that we haven’t yet covered completing the square, a technique important for solving quadratic equations, and also in several other applications. We’ll see the traditional method, and a modified method that avoids fractions, including a nice alternative to the quadratic formula.