/Tag: Polynomials
15 12, 2018

Sum & Products of Roots

By |2018-12-18T17:18:28+10:00December 15th, 2018|Tags: , , |Comments Off on Sum & Products of Roots

Sum & Products of Roots Go to the Polynomials Forum to see more questions or ask your own Formulas used in Sum & Products of Roots Sum & Products Roots $$ax^2+bx+c=0$$ $$\alpha+\beta=-\frac{b}{a}$$ $$\alpha\beta=\frac{c}{a}$$ $$\alpha^2+\beta^2=(\alpha+\beta)^2-2(\alpha\beta)$$ $$\alpha^3+\beta^3=(\alpha+\beta)^3-3(\alpha\beta)(\alpha+\beta)$$ $$ax^3+bx^2+cx+d=0$$ $$\alpha+\beta+\gamma=-\frac{b}{a}$$ $$\alpha\beta+\alpha\gamma+\beta\gamma=\frac{c}{a}$$ $$\alpha\beta\gamma=-\frac{d}{a}$$ $$\alpha^2+\beta^2+\gamma^2=(\alpha+\beta+\gamma)^2-2(\alpha\beta+\alpha\gamma+\beta\gamma)$$ $${\alpha ^3} + {\beta ^3} + {\gamma ^3} = [...]

13 11, 2018

de Moivre’s Theorem

By |2018-11-13T17:01:58+10:00November 13th, 2018|Tags: , |Comments Off on de Moivre’s Theorem

de Moivre's Theorem Go to the Polynomials Forum to see more questions or ask your own Formulas used in de Moivre's Theorem $$z=r(\cos\theta+i\sin\theta)$$ $${z^n} = {r^n}(\cos n\theta + i\sin \;n\theta )$$ $${r^n}(\cos \;n\theta + i\sin n\theta ) = {r^n}{(\cos \theta + i\sin \theta )^2}$$ $$\cos n\theta + i\sin n\theta \; [...]

8 02, 2017

Zeroes & Multiplicity

By |2019-02-11T18:36:46+10:00February 8th, 2017|Tags: , , |0 Comments

Zeroes/Roots & Multiplicity Go to the Forum to see more questions or ask your own Formulas Used in Roots & Multiplicity zeroes, are the roots, or solutions to the equation P(x) Number of Roots The maximum number of roots a Polynomial can have is equal to the degree of that polynomial If the [...]

17 01, 2017

Forum

By |2017-01-17T07:30:59+10:00January 17th, 2017|Tags: , , |Comments Off on Forum

Extension 2 Polynomials Forum Rules of the Forumbe respectful of other membersno profanitypost questions in appropriate areasONE question per post

17 01, 2017

Polynomials

By |2018-12-15T20:00:24+10:00January 17th, 2017|Tags: , |0 Comments

Polynomials Go to the Polynomials forum to see more questions or ask your own Topics Covered in Polynomials Division Transformation de Moivre's Theorem Sum & Products of Roots Formulas Used in Polynomials Division Transformation P(x) ≡ D(x).Q(x) + R(x) where deg [...]

17 06, 2016

Polynomials

By |2016-11-28T07:24:44+10:00June 17th, 2016|Tags: , |0 Comments

Polynomials Go to the Polynomials Forum to see more questions or ask your own Topics Covered in Polynomials Determining Polynomails Evaluating Polynomials Finding Unknowns Expending & Simplifying Dividing Remainder Theorem Factor Theorem Factorising & Zeros Sketching Graphs [...]

20 08, 2015

Newtons Method

By |2019-02-12T12:09:53+10:00August 20th, 2015|Tags: , , |0 Comments

Newtons Method $$x_1=x_0-\frac{f(x_0)}{f'(x_0)}$$ worked examples Starting with x = 2, find a better approximation to the root of f(x) = x3 + 3x - 18, correct to two decimal places. f'(x) = 3x2 + 3 find f'(x) $${x_1} = 2 - \frac{{2^3 + 3\times2 - 18}}{{3\times2^2 + 3}}$$ using [...]

Show Buttons
Hide Buttons