1.3 - 1.3 QUADRATIC EQUATIONS Objectives In this section we...

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1.3 QUADRATIC EQUATIONSQUADRATIC EQUATIONS1.3 3 QUADRATIC EQUATIONSQUADRATIC EQUATIONS
Objectives:Objectives:In this section, we learn about:¾Solving Quadratic Equations by Factoring¾Solving Quadratic Equations by Taking Square Roots¾Solving Quadratic Equations by Completing the Square¾Solving Quadratic Equations by Using the Quadratic Formula¾ThDiiitfQdtiEti¾The Discriminant of a Quadratic Equation¾Application of Quadratic EquationBassam Al Absi210/23/2007
Definition of a Quadratic EquationﺔﻟدﺎﻌﻤﻟاﺔﻴﻌﻴﺑﺮﺘﻟاDefinition of a Quadratic Equation ﻴ ﻴﺑﺮA quadratic equation in x is an equation that can be written in thestandard formax2+ b x + c = 0where a, b,and care real numbers with a 0.A quadratic equation in x is also called a second-degree polynomial equation in x.3Bassam Al Absi10/23/2007
The Zero Product PrincipleIf the product of two algebraic expressions is zero, then at least one of the factors is equal to zero.If A · B = 0 , then A = 0 or B= 0.zeroproduct4Bassam Al Absi10/23/2007
Qdiibld bQuadratic equations can be solved by:1. Factoring2 Taking square roots of both sides2. Taking square roots of both sides 3. Completing the square4. Using the quadratic formulaBassam Al Absi510/23/2007
1Solving a Quadratic Equation by Factoring1. Solving a Quadratic Equation by Factoringa)If necessary, rewrite the equation in the form ax2+ bx + c = 0, moving all terms to one side, thereby obtaining zero on the other side.b)Factor.c)Apply thezero product principlesetting each factorc)Apply the zero-product principle, setting each factor equal to zero.S lhiid)Solve the equations in step c.6Bassam Al Absi10/23/2007
Ex 1Factor and Solve the quadratic equation:01072=+xxEx 1Factor and Solve the quadratic equation:0107=+xxSol:1. Solving a Quadratic Equation by Factoring0)5()2(=xxa)If necessary, rewrite the equation in the form ax2+ bx + c = 0, 20 or 50xx==moving all terms to one side, thereby obtaining zero on the other side.b)Factor.25c)Apply the zero-product principle, setting each factor equal to zero.d)Solve the equations in2 5xx==d)Solve the equations in step c.7Bassam Al Absi10/23/2007
Sol:Ex 2Solve the quadratic equation4x2= 2xSol:4x2– 2x= 0()1. Solving a Quadratic Equation by Factoring2x(2x–1) = 02x= 0 or 2x– 1 = 0a)If necessary, rewrite the equation in the form ax2+ bx + c = 0, moving all terms to one x= 0x= 12

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