Types of Algebraic Equations

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Algebra LINEAR EQUATIONS The root(s) of an equation (conditional equation) is any value(s) of the literal number(s) in the equation that makes the equation true.   Thus, 1 is the root of the equation 3x  + 5 = 8 because = 1 makes the equation true.   To solve an algebraic equation means to find the root(s) of the equation. The  application  of  algebra  is  practical  because  many  physical  problems  can  be  solved  using algebraic equations.   For example, pressure is defined as the force that is applied divided by the area  over  which  it  is  applied.    Using  the  literal  numbers  P  (to  represent  the  pressure),  F  (to represent the force), and (to represent the area over which the force is applied), this physical relationship can be written as the algebraic equation .  When the numerical values of the P F A force,  F, and the area,  A, are known at a particular time, the pressure,  P, can be computed by solving  this  algebraic  equation.   Although  this  is  a  straightforward  application of  an  algebraic equation  to  the  solution of  a  physical  problem,  it  illustrates  the  general approach  that  is  used. Almost all physical problems are solved using this approach. Types of Algebraic Equations The letters in algebraic equations are referred to as unknowns.   Thus,  x  is the unknown in the equation  3x  +  5  =  8.    Algebraic  equations  can  have  any  number  of  unknowns.    The  name unknown arises because letters are substituted for the numerical values that are not known in a problem. The number of unknowns in a problem determines the number of equations needed to solve for the numerical values of the unknowns.  Problems involving one unknown can be solved with one equation, problems involving two unknowns require two independent equations, and so on. The degree of an equation depends on the power of the unknowns.   The degree of an algebraic term is equivalent to the exponent of the unknown.  Thus, the term 3is a first degree term; 3x2 is a second degree term, and 3x3 is a third degree term.   The degree of an equation is the same as the highest degree term.   Linear or first degree equations contain no terms higher than first degree.  Thus, 2+ 3 = 9 is a linear equation.   Quadratic or second degree equations contain up to second degree terms, but no higher.  Thus, x2 + 3= 6, is a quadratic equation.  Cubic or third degree equations contain up to third degree terms, but no higher.  Thus, 4x3 + 3= 12 is a cubic equation. The degree of an equation determines the number of roots of the equation.  Linear equations have one root, quadratic equations have two roots, and so on.   In general, the number of roots of any equation is the same as the degree of the equation. Rev. 0 Page 5 MA-02


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