Root-finding algorithms | Theorems about polynomials

Rational root theorem

In algebra, the rational root theorem (or rational root test, rational zero theorem, rational zero test or p/q theorem) states a constraint on rational solutions of a polynomial equation with integer coefficients and . Solutions of the equation are also called roots or zeroes of the polynomial on the left side. The theorem states that each rational solution x = p⁄q, written in lowest terms so that p and q are relatively prime, satisfies: * p is an integer factor of the constant term a0, and * q is an integer factor of the leading coefficient an. The rational root theorem is a special case (for a single linear factor) of Gauss's lemma on the factorization of polynomials. The integral root theorem is the special case of the rational root theorem when the leading coefficient is an = 1. (Wikipedia).

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Rational Roots Theorem

Rational Roots Theorem In this video, I give you a cool theorem that helps us factor out polynomials, provided that they have a rational root, enjoy! Rational Roots Theorem Proof: https://youtu.be/zMQ-E7D7t30 Check out my Real Numbers Playlist: https://www.youtube.com/playlist?list=PLJ

From playlist Precalculus

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Rational or Irrational ?

Rational Roots Theorem Application In this video, I give a neat application of the rational roots theorem, by showing that square root of( 2 + square root of 2) is in fact irrational. Of course there are faster ways of doing this, but this one is more systematic. Enjoy! Check out my Real

From playlist Real Numbers

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Rational Roots Proof

Rational Roots Theorem Proof In this video, I prove the rational roots theorem, which is a neat way of finding rational roots of polynomials. A little algebra delight to sweeten the day! Rational Roots Example: https://youtu.be/afCJ3ehcOFY Check out my Real Numbers Playlist: https://www

From playlist Real Numbers

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Let’s Learn The Rational Root Theorem….Step-by-Step….

TabletClass Math: https://tcmathacademy.com/ Math help with solving a polynomial equation using the rational root theorem. For more math help to include math lessons, practice problems and math tutorials check out my full math help program at https://tcmathacademy.com/ Math Notes:

From playlist Pre-Calculus / Trigonometry

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Pre-Calculus - Rational roots theorem for polynomials

This video covers the rational roots theorem for polynomials. This theorem is important because when finding zeros, it gives us a list of possible rational zeros we can try. http://www.mysecretmathtutor.com

From playlist Pre-Calculus

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Rationalizing a denominator - free math help on homework, 5root(5) / 2root(10)

👉 Learn how to find the square root of rational numbers. To find the square root of a rational number, we first express the rational number as the square root of the numerator divided by the square root of the denominator and simplify. Where the rational number can divide, we divide the nu

From playlist Divide Square Root Expressions

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Rational Roots Polynomial Division

TabletClass Math http://www.tabletclass.com complete courses in middle and high school math. This videos explains the rational roots of a polynomials

From playlist Algebra 2

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How to simplify the root of a rational expression

👉 Learn how to find the square root of rational expressions. To find the square root of a rational expression, we first express the rational expression as the square root of the numerator divided by the square root of the denominator. Next, we rationalize the rational expression by multipl

From playlist Simplify the square root with multiple fractions

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Learn how to rationalize the denominator to simplify an expression

👉 Learn how to find the square root of rational expressions. To find the square root of a rational expression, we first express the rational expression as the square root of the numerator divided by the square root of the denominator. Next we rationalize the rational expression by multiply

From playlist Divide Square Root Expressions

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Irrational Roots

iNEW (Christmas 2019). Two ways to support Mathologer Mathologer Patreon: https://www.patreon.com/mathologer Mathologer PayPal: paypal.me/mathologer (see the Patreon page for details) For the final video for 2018 we return to obsessing about irrational numbers. Everybody knows that root

From playlist Recent videos

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Sums of Two Cubes by Ari Shnidman

PROGRAM ELLIPTIC CURVES AND THE SPECIAL VALUES OF L-FUNCTIONS (HYBRID) ORGANIZERS: Ashay Burungale (CalTech/UT Austin, USA), Haruzo Hida (UCLA), Somnath Jha (IIT Kanpur) and Ye Tian (MCM, CAS) DATE: 08 August 2022 to 19 August 2022 VENUE: Ramanujan Lecture Hall and online The program pla

From playlist ELLIPTIC CURVES AND THE SPECIAL VALUES OF L-FUNCTIONS (2022)

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Lec 11. Finding the Roots of a Polynomial College Algebra with Dennis Allison

See full course at: https://cosmolearning.org/courses/college-algebra-pre-calculus-with-dennis-allison/ Video taken from: http://desource.uvu.edu/videos/math1050.php Lecture by Dennis Allison from Utah Valley University.

From playlist UVU: College Algebra with Dennis Allison | CosmoLearning Math

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Proofs by contradiction -- Proofs

This lecture is on Introduction to Higher Mathematics (Proofs). For more see http://calculus123.com.

From playlist Proofs

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Prove that sqrt(19) is irrational

Just a short video where I prove that the square root of 19 is irrational. I do this using the Rational Roots Theorem. Note that 19 is prime so you can easily replace 19 with any other prime number and the proof is the same. If you enjoyed this video please consider liking, sharing, and s

From playlist Math Proofs for Beginners

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How do you simplify the root of rational terms with variables

👉 Learn how to find the square root of rational expressions. To find the square root of a rational expression, we first express the rational expression as the square root of the numerator divided by the square root of the denominator. Next, we rationalize the rational expression by multipl

From playlist Simplify the square root with multiple fractions

Related pages

Quadratic formula | Fundamental theorem of algebra | Coefficient | Horner's method | Polynomial long division | Polynomial | Greatest common divisor | Rational number | Equation solving | Algebra | Complex plane | Integer | Divisor | Cubic function | Constant term | Descartes' rule of signs | Algebraic expression | Euclid's lemma | Eisenstein's criterion | Integrally closed domain | Gauss–Lucas theorem | Cubic equation | Irrational number