Solving quadratics and cubics approximately | Real numbers and limits Math Foundations 85

We review the standard formulas for solving quadratic and cubic equations, the latter going back to work in the 1500's by del Ferro, Tartaglia and Cardano, and pointing out that in reality these formulas only generate approximate solutions, at least in general. We also connect both formulas with Newton's method to solve an example quadratic and an example cubic, at least approximately. This lecture is part of the MathFoundations series, which tries to lay out proper foundations for mathematics, and will not shy away from discussing the serious logical difficulties entwined in modern pure mathematics. Video Content: 00:00 Intro to quadratic and cubic equations 5:58 Making a quadratic equation with solutions 9:17 Solving the quadratic equation 13:26 Using quadratic formula 16:15 Cubic equation 21:20 Creating a cubic equation with solutions 27:23 How Newton's method tackles the same cubic equation 30:51 Newton's method and algebraic curves ************ Research Gate page: https://www.researchgate.net/profile/... Blog: http://njwildberger.com/ Online courses at openlearning.com (currently Algebraic Calculus One): https://www.openlearning.com/courses/... Please join us for an exciting new approach to one of mathematics' most important subjects! Patreon:   / njwildberger   Your support would be much appreciated. Wild Egg Maths YT channel: https://www.youtube.com/channel/UCriF... Insights into Mathematics Playlists:    • The Algebra of Boole, Logic and Circuit An...   (31 videos)    • Box Arithmetic: a new framework for Mathem...   (18 videos)    • Hypergroups and Diffusion Symmetry: an int...   (6 videos)    • Rational Trigonometry for maths, physics a...   (4 videos)    • Sociology and Pure Maths   (44 videos)    • Old Babylonian mathematics and Plimpton 322   (8 videos)    • Math Foundations   (226 videos)    • Math Seminars N J Wildberger   (26 videos)    • Math History (ancient to modern)   (45 videos)    • Geometric Linear Algebra   (43 videos)    • Algebraic Topology   (40 videos)    • Universal Hyperbolic Geometry   (55 videos)    • Differential Geometry   (34 videos)    • Elementary Probability and Statistics   (8 videos)    • Math Terminology for Incoming Uni Students   (9 videos)    • Famous Math Problems   ( 46 videos)    • Elementary Mathematics Explained (K-6)   (40 videos)    • Ancient Mathematics and insights of Howard...   (7 videos)    • Wild West Banking: A mathematician goes We...   (7 videos)    • Playing Go: the ancient oriental board game   (19 videos)    • Maths and Music   (21 videos)    • Year 9 Mathematics (review fractions, deci...   (10 videos)    • Wild Trig: An introduction to Rational Tri...   (94 videos) Wild Egg Maths Playlists:    • Intro to Algebraic Calculus with Box Arith...   (4 videos)    • Classical to Quantum (for Members)   (64 videos)    • Solving Polynomial Equations and the Geode...   (45 videos)    • De Casteljau Bezier curves and associated ...   (20 videos)    • Exploring q-series (for Members)   (8 videos)    • Six: A mathematical exploration   (9 videos)    • Algebraic Calculus One: a new foundation f...   (52 videos)    • Advice to prospective research mathematici...   (9 videos)    • The Hexagrammum Mysticum: a Geometric Gem ...   (14 videos)    • Algebraic Calculus Two   (8 videos)    • Special (Polynomial) Functions and Maxel N...   (25 videos)    • Dynamics on Graphs: The ADE Phenomenon & B...   (30 videos)