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1.5_bzca5e - Section 1.5 Quadratic Equations Definition of...

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Section 1.5 Quadratic Equations
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2 Definition of a Quadratic Equation A quadratic equation in x is an equation that can be written in the general form 0, where a, b, and c are real numbers, with a 0. A quadratic equation in x is a ax bx x + + = lso called a second-degree polynomial equation in x.
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Solving Quadratic Equations by Factoring
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The Zero-Product 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
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2 Solving a Quadratic Equation by Factoring 1. If necessary, rewrite the equation in the general form ax +bx+c=0, moving all terms to one side, thereby obtaining zero on the other side. 2. Factor completely. 3. Apply the zero-product principle, setting each factor containing a variable equal to zero. 4. Solve the equations in step 3. 5. Check the solutions in the original equation
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Example 2 5 6 0 x x - + = Solve by factoring:
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Example Solve by factoring: 2 3 40 x x + =
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Example Solve by factoring: 2 2 11 15 0 x x - + =
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Graphing Calculator The real solutions of a quadratic equation
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