0 NEGATIVE Roots? 🚫 The Descartes "P(-x)" TRICK for the Number of Negative Real Roots скачать в хорошем качестве

0 NEGATIVE Roots? 🚫 The Descartes "P(-x)" TRICK for the Number of Negative Real Roots

Stop testing negative numbers! 🛑 In this clip, we use Descartes' Rule of Signs to find the number of negative real roots for P(x) = 2x^4 - 17x^3 + 53x^2 - 72x + 36. By replacing x with -x, we essentially flip the graph across the y-axis. The Shortcut: Even powers (x^4, x^2): The sign stays the SAME. Odd powers (x^3, x): The sign FLIPS. After the transformation, we see zero sign changes in P(-x) = 2x^4 + 17x^3 + 53x^2 + 72x + 36. This proves there are ZERO negative real roots for the original polynomial because there are ZERO positive real roots of P(-x). Time to focus only on the positive numbers! #math #precalculus #descartesruleofsigns #algebra2 #polynomials #mathshortcuts #studyguide #mathtips #mathhelp How Many NEGATIVE Real Roots? Apply Descartes’ Rule of Signs to P(-x) 📖 Precalculus, by Stewart, Redlin, and Watson: https://amzn.to/4sIzIE9. Links and resources =============================== 🔴 Subscribe to Bill Kinney Math: https://www.youtube.com/user/billkinn... 🔴 Subscribe to my Math Blog, Infinity is Really Big: https://infinityisreallybig.com/ 🔴 Follow me on LinkedIn:   / bill-kinney-a1246610   🔴 Follow me on Twitter:   / billkinneymath   🔴 Follow me on Instagram:   / billkinneymath   🔴 You can support me by buying "Infinite Powers, How Calculus Reveals the Secrets of the Universe", by Steven Strogatz, or anything else you want to buy, starting from this link: https://amzn.to/3eXEmuA. 🔴 Check out my artist son Tyler Kinney's website: https://www.tylertkinney.co/ 🔴 Desiring God website: https://www.desiringgod.org/ AMAZON ASSOCIATE As an Amazon Associate I earn from qualifying purchases.