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Quadratic EquationsA quadratic equation in x is an equation that can be written in the standard from ax^{2} + bx +c = 0 where a, b, and c are real numbers with a ≠ 0. A quadratic equation in x is also called a seconddegree polynomial equation in x The ZeroProduct Principle If the product of two algebraic expressions is zero, then at least one of the factors is equal to zero. .If AB = 0, then A = 0 or B = 0. Solving a Quadratic Equation by Factoring 2.Factor. 3. Apply the zeroproduct principle, setting each factor equal to zero. 4. Solve the equations in step 3. 5. Check the solutions in the original equation. Ex 1 Solve by factoring:
Solution Continued Solution set is Practice Exercises Solve: Answers 1. Solution set 2.Solution set The Square Root Method
Ex 2 Solve by the square root method: Solution Solution set: Completing the Square If x^{2} + bx is a binomial, then by adding , which is the square of half the coefficient of x, a perfect square trinomial will result.. Ex 3 What term should be added to the binomial so that it becomes a perfect square trinomial? Add the constant Factor the trinomial Practice Exercise Determine the constant that should be added to the binomial so that it becomes a perfect square trinomial. Then factor the trinomial Answer
