Algebra QUADRATIC EQUATIONSQUADRATIC EQUATIONSThis chapter covers solving for unknowns using quadratic equations.EO 1.3 APPLY the quadratic formula to solve for an unknown.TypesofQuadraticEquationsA quadratic equation is an equation containing the second power of an unknown but no higherpower. The equation x^{2} - 5x + 6 = 0 is a quadratic equation. A quadratic equation has two roots,both of which satisfy the equation. The two roots of the quadratic equation x^{2} - 5x + 6 = 0 arex = 2 and x = 3. Substituting either of these values for x in the equation makes it true.The general form of a quadratic equation is the following:ax^{2}- bx + c = 0 (2-1)The a represents the numerical coefficient of x^{2}, b represents the numerical coefficient of x, andc represents the constant numerical term. One or both of the last two numerical coefficients maybe zero. The numerical coefficient a cannot be zero. If b=0, then the quadratic equation istermed a "pure" quadratic equation. If the equation contains both an x and x^{2} term, then it is a"complete" quadratic equation. The numerical coefficient c may or may not be zero in acomplete quadratic equation. Thus, x^{2} + 5x + 6 = 0 and 2x^{2}- 5x = 0 are complete quadraticequations.SolvingQuadraticEquationsThe four axioms used in solving linear equations are also used in solving quadratic equations.However, there are certain additional rules used when solving quadratic equations. There arethree different techniques used for solving quadratic equations: taking the square root, factoring,and the Quadratic Formula. Of these three techniques, only the Quadratic Formula will solve allquadratic equations. The other two techniques can be used only in certain cases. To determinewhich technique can be used, the equation must be written in general form:ax^{2}+ bx + c = 0 (2-1)If the equation is a pure quadratic equation, it can be solved by taking the square root. If thenumerical constant c is zero, equation 2-1 can be solved by factoring. Certain other equationscan also be solved by factoring.Rev. 0 Page 17 MA-02