1300_section4o4

1300_section4o4 - Math 1300 Section 4.4 Notes Solving...

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Math 1300 Section 4.4 Notes 1 Solving Equations by Factoring Definition: The zero-product property says that if a and b are numbers such that ab = 0, then a = 0 or b = 0 (or both). Definition: A quadratic equation is an equation that can be written as ax 2 + bx + c = 0, where a , b , and c are numbers and a 0. Solving Quadratic Equations To solve a quadratic equation, we must find all possible values for x that make ax 2 + bx + c = 0. Factoring is usually a helpful way to solve quadratic equations. To use factoring, move all nonzero terms to one side of the equal sign so that the other side is zero. Then use the zero-product property. Examples: 1. Solve the equation x 2 – 5 x – 24 = 0. Only the left-hand side (LHS) of the equation has nonzero terms, so no movement of terms is necessary. Factor the LHS and use the zero-product property (ZPP): x 2 – 5 x – 24 = 0 Factor : ( x + 3)( x – 8) = 0 ZPP : x + 3 = 0 or x – 8 = 0 Solve for x : x = –3 or x = 8 2. Solve 2 x 2 + 18 x – 72 = 0 for x . All nonzero terms are on the LHS, so no movement of terms is needed. 2
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1300_section4o4 - Math 1300 Section 4.4 Notes Solving...

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