Stage 31 · Complex Numbers

31.6.4 The Full Picture of a Quadratic's Roots

31.6 Complex Numbers and Equations: Letting Every Root Appear

Point 4 of 5

31.6.4 The Full Picture of a Quadratic's Roots

Core idea

Picture this: whether Δ is positive, zero, or negative, a quadratic always has two roots (counting a repeated one); complex numbers finally make "the number of roots" perfectly uniform

Module goal. We use complex numbers to complete the roots of real-coefficient equations, reclaiming what a negative discriminant used to cost us, and paving the way for counting and polynomials ahead
eastmath.com · 31.6 Complex Numbers and Equations: Letting Every Root Appear · 31.6.4 The Full Picture of a Quadratic's Roots