1.4 QuadEqs - 1.4 QUADRATIC EQUATIONS Objectives In this...

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22/11/143111.4 QUADRATIC EQUATIONSObjectives:Solving Quadratic Equations by FactoringSolving Quadratic Equations by Taking Square RootsSolving Quadratic Equations by Completing the SquareSolving Quadratic Equations by Using the Quadratic FormulaThe Discriminant of a Quadratic EquationApplication of Quadratic EquationBassam Al AbsiIn this section, we learn about:10/29/20102
22/11/14312Definition of a Quadratic Equation ةيعيبرتلا ةلداعملاA quadratic equation in x is an equation that can be written in thestandard forma x2+ b x + c = 0where a, b,and care real numbers with a 0.Bassam Al Absi10/29/20103Quadratic Equations can be solved by:1. Factoring2. Taking square roots of both sides 3. Completing the square4. Using the quadratic formulaEx 1Factor and Solve the quadratic equation:01072xxSol:1. Solving a Quadratic Equation by Factoringc)Apply the zero-product principle, setting each factor equal to zero.d)Solve the equations in step c.B= 0
22/11/14313Sol:4x22x= 02x(2x1) = 02x= 0 or 2x1 = 0x= 0x= 12A check shows that the solution set for the given equation is {0, 1 2}.Ex 2 Solve the quadratic equation4x2= 2x1. 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 the zero-product principle,setting each factor equal to zero.d)Solve the equations in step c.Bassam Al Absi10/29/20105If A · B = 0 , then A = 0 or B= 0zeroproductSol:x2 +2x8 = 0( x + 4 ) ( x 2) = 0x + 4 = 0 or x 2 = 0x= 4orx= 2A check shows that the solution set for the given equation is {4, 2 }Ex 3 Solve the quadratic equation( x

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