AlgebraLINEAR EQUATIONSThe root(s) of an equation (conditional equation) is any value(s) of the literal number(s) in theequation that makes the equation true. Thus, 1 is the root of the equation 3x + 5 = 8 becausex = 1 makes the equation true. To solve an algebraic equation means to find the root(s) of theequation.The application of algebra is practical because many physical problems can be solved usingalgebraic equations. For example, pressure is defined as the force that is applied divided by thearea over which it is applied. Using the literal numbers P (to represent the pressure), F (torepresent the force), and A (to represent the area over which the force is applied), this physicalrelationship can be written as the algebraic equation . When the numerical values of thePFAforce, F, and the area, A, are known at a particular time, the pressure, P, can be computed bysolving this algebraic equation. Although this is a straightforward application of an algebraicequation to the solution of a physical problem, it illustrates the general approach that is used.Almost all physical problems are solved using this approach.TypesofAlgebraicEquationsThe letters in algebraic equations are referred to as unknowns. Thus, x is the unknown in theequation 3x + 5 = 8. Algebraic equations can have any number of unknowns. The nameunknown arises because letters are substituted for the numerical values that are not known in aproblem.The number of unknowns in a problem determines the number of equations needed to solve forthe numerical values of the unknowns. Problems involving one unknown can be solved with oneequation, 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 algebraicterm is equivalent to the exponent of the unknown. Thus, the term 3x is a first degree term; 3x^{2}is a second degree term, and 3x^{3} is a third degree term. The degree of an equation is the sameas the highest degree term. Linear or first degree equations contain no terms higher than firstdegree. Thus, 2x + 3 = 9 is a linear equation. Quadratic or second degree equations contain upto second degree terms, but no higher. Thus, x^{2} + 3x = 6, is a quadratic equation. Cubic or thirddegree equations contain up to third degree terms, but no higher. Thus, 4x^{3} + 3x = 12 is a cubicequation.The degree of an equation determines the number of roots of the equation. Linear equations haveone root, quadratic equations have two roots, and so on. In general, the number of roots of anyequation is the same as the degree of the equation.Rev. 0 Page 5 MA-02