3 1 Solving Linear Equations 2 3 2 Solving Quadratic Equations 13 3 3 Solving Polynomial Equations 31 3 4 Solving Simultaneous Linear Equations 42
| Previous PDF | Next PDF |
[PDF] Solving equations: linear, quadratic,polynomial,simultaneous linear
3 1 Solving Linear Equations 2 3 2 Solving Quadratic Equations 13 3 3 Solving Polynomial Equations 31 3 4 Solving Simultaneous Linear Equations 42
[PDF] Equations Linear, Quadratic, Cubic and Higher Orders
to solve simultaneous linear and quadratic equations • nature of roots The higher degree equations are also called higher degree polynomials or polynomial
[PDF] Module M14 Solving equations
Simultaneous linear equations 2 4 Graphical In Section 3 the discussion is extended to the solution of quadratic equations by Section 4 graphical and numerical procedures for solving polynomial equations are described The first thing
[PDF] Unit 4 Polynomials and Quadratic Functions Algebra - Long Beach
23 jui 2017 · Factoring polynomials breaks apart more complex expressions into smaller, more easily Systems consisting of a linear equation and a quadratic equation can be solved Using algebraic methods, such as substitution and
[PDF] Maxima by Example: Ch4: Solving Equations ∗ - CSULB
4 1 3 General Quadratic Equation or Function linsolve solves a system of simultaneous linear equations for the speci ed variables and returns a list of the solutions allroots nds all the real and complex roots of a real univariate polynomial
6 Polynomial Equations
ination could be adapted to simultaneous polynomial equations in two or be found by solving a series of linear or quadratic equations, which is why they
[PDF] Chapter One
1 jui 2016 · Objective 1: Solving Higher Order Polynomial Equations Linear equations and quadratic equations are both examples of polynomial equations of first and second degree, quadratic equation by using a substitution
[PDF] fx-991EX/fx-570EX - CASIO
SIMULTANEOUS EQUATIONS From the Main Menu, use To solve the following system of simultaneous equations , select 1(Simul To start solving polynomial equations, in the Equation/Func icon, the quadratic template, and press p
[PDF] linear quadratic systems elimination
[PDF] linearity of fourier transform
[PDF] lingua lecturas en español
[PDF] linguistic adaptation
[PDF] linguistic signals of power and solidarity
[PDF] linguistics ap human geography
[PDF] linguistics of american sign language 5th edition
[PDF] linguistics of american sign language 5th edition answers
[PDF] linguistics of american sign language 5th edition pdf
[PDF] linguistics of american sign language an introduction
[PDF] linguistics of american sign language an introduction pdf
[PDF] linguistics of american sign language assignment 11
[PDF] linguistics of american sign language homework answers
[PDF] link and phelan's theory of the fundamental causes of health inequality
![[PDF] Solving equations: linear, quadratic,polynomial,simultaneous linear](https://pdfprof.com/Listes/39/92554-39WB03-all.pdf.pdf.jpg "[PDF] Solving equations: linear, quadratic,polynomial,simultaneous linear")
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a!E&A()BA2!Z*(25#4()$*!]!Cb&4()$*-3!Z*2b&4A)()2-!X!"4#()4A!J#4"()$*-!.8!L)++2#2*()4A!'2"($#!K4A"&A&-!c!M#)5$*$62(#;!.d!Z*(25#4A!'2"($#!K4A"&A&-!1!J&*"()$*-!4*%!E$%2AA)*5!]/!Z*(#$%&"()$*!($!<&62#)"4A!E2(,$%-!Q!CRB$*2*()4A!4*%!D$54#)(,6)"!J&*"()$*-!]0!<&62#)"4A!E2(,$%-!$+!VBB#$R)64()$*!a!E4(#)"2-!].!<&62#)"4A!Z*)()4A!'4A&2!"#$:A26-!8!E4(#)R!P$A&()$*!$+!Cb&4()$*-!]]!<&62#)"4A!W$&*%4#;!'4A&2!"#$:A26-!d!'2"($#-!]c!E$%2AA)*5!E$()$*!0/!K$6BA2R!<&6:2#-!]1!P2(-!4*%!"#$:4:)A)(;!00!L)++2#2*()4()$*!]Q!L2-"#)B()72!P(4()-()"-!0.!VBBA)"4()$*-!$+!L)++2#2*()4()$*!]a!L)-"#2(2!"#$:4:)A)(;!L)-(#):&()$*-!0]!Z*(25#4()$*!]8!K$*()*&$&-!"#$:4:)A)(;!L)-(#):&()$*-!0c!VBBA)"4()$*-!$+!Z*(25#4()$*!0!]d!M,2!<$#64A!L)-(#):&()$*!01!VBBA)"4()$*-!$+!Z*(25#4()$*!.!c/!P46BA)*5!L)-(#):&()$*-!4*%!C-()64()$*!0Q!P2b&2*"2-!4*%!P2#)2-!c0!@;B$(,2-)-!M2-()*5!0a!K$*)"-!4*%!"$A4#!K$$#%)*4(2-!c.!Y$$%*2--!$+!J)(!4*%!K$*()*52*";!M4:A2-!08!J&*"()$*-!$+!P272#4A!'4#)4:A2-!c]!U25#2--)$*!4*%!K$##2A4()$*!0d!L)++2#2*()4A!Cb&4()$*-!cc!V*4A;-)-!$+!'4#)4*"2!./!D4BA4"2!M#4*-+$#6-!c1!<$*GB4#462(#)"!P(4()-()"-!.0!eGM#4*-+$#6-!cQ!U2A)4:)A)(;!4*%![&4A)(;!K$*(#$A!..!C)52*74A&2-!4*%!C)52*72"($#-!ca!E4(,264()"-!4*%!",;-)"-!E)-"2AA4*;!.]!J$&#)2#!P2#)2-!c8!C*5)*22#)*5!K4-2!P(&%;!.c!J$&#)2#!M#4*-+$#6-!cd!P(&%2*(f-!Y&)%2!.1!"4#()4A!L)++2#2*()4A!Cb&4()$*-!1/!M&($#f-!Y&)%2!!g!K$B;#)5,(!!D$&5,:$#$&5,!I*)72#-)(;3!./01!
ContentsContents
& Partial FractionsEquations, Inequalities3.1 Solving Linear Equations 23.2 Solving Quadratic Equations 13
3.3 Solving Polynomial Equations 31
3.4 Solving Simultaneous Linear Equations 42
3.5 Solving Inequalities 50
3.6 Partial Fractions 60
Learning
In this Workbook you will learn about solving single equations, mainly linear and quadratic, but also cubic and higher degree, and also simultaneous linear equations. Such equations often arise as part of a more complicated problem. In order to gain confidence in mathematics you will need to be thoroughly familiar with these basis topics. You will also study how to manipulate inequalities. You will also be introduced to partial fractions which will enable you to re-express an algebraic fraction in terms of simpler fractions. This will prove to be extremely useful in later studies on integration. outcomesSolving Linear
Equations
3.1Introduction
Many problems in engineering reduce to the solution of an equation or a set of equations. An equation
is a type of mathematical expression which contains one or more unknown quantities which you will be required to nd. In this Section we consider a particular type of equation which contains a single unknown quantity, and is known as a linear equation. Later Sections will describe techniques for solving other types of equations.Prerequisites
Before starting this Section you should:::be able to add, subtract, multiply and divide fractions be able to transpose formulaeLearning Outcomes
On completion you should be able to:::recognise and solve a linear equation2HELM (2015):
Workbook 3: Equations, Inequalities & Partial Fractions1. Linear equations
Key Point 1
Alinear equationis an equation of the form
ax+b= 0a6= 0whereaandbare known numbers andxrepresents an unknown quantity to be found.In the equationax+b= 0, the numberais called thecoecient ofx, and the numberbis called
theconstant term.The following are examples of linear equations
3x+ 4 = 0;2x+ 3 = 0;12
x3 = 0 Note that the unknown,x, appears only to the rst power, that is asx, and not asx2,px,x1=2etc. Linear equations often appear in a non-standard form, and also dierent letters are sometimes used for the unknown quantity. For example2x=x+ 1 3t7 = 17;13 = 3z+ 1;112
y= 3 21:5 = 0 are all examples of linear equations. Where necessary the equations can be rearranged and written in the formax+b= 0. We will explain how to do this later in this Section. TaskWhich of the following are linear equations and which are not linear? (a)3x+ 7 = 0, (b)3t+ 17 = 0, (c)3x2+ 7 = 0, (d)5p= 0 The equations which can be written in the formax+b= 0are linear.Your solution (a) (b) (c) (d)Answer(a) linear inx(b) linear int(c) non-linear - quadratic inx(d) linear inp, constant is zeroTo solve a linear equation means to nd the value ofxthat can be substituted into the equation so
that the left-hand side equals the right-hand side. Any such value obtained is known as asolution orrootof the equation and the value ofxis said tosatisfythe equation.