Solving Polynomial Equations

Abstract Algebra · Axiom Academy

A 400-year mathematical journey from triumph to impossibility. Discover why some equations have no formula! Mathematicians spent centuries searching for formulas to solve polynomial equations. Let's trace this incredible journey through time. You already know this one! The quadratic formula solves any equation of the form ax² + bx + c = 0. In 1545, Gerolamo Cardano published the cubic formula. It's much more complex, but follows the same pattern! Degree 4: Ferrari's Achievement The same year Cardano published his work, his student Lodovico Ferrari solved the quartic. Surely quintics would be next? Degree 5: The Impossible Dream Abel proved it was impossible, but why ? What's special about degree 5? This question leads to one of mathematics' most beautiful theories...

This is the written version of the interactive lesson above. See the full Abstract Algebra course.