MAT100H5 Lecture Notes - Lecture 9: Algebraic Equation
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Solve the following polynomial equations for (cid:1876). (a) (cid:1876)(cid:2871)=(cid:886)(cid:1876) (b) (cid:884)(cid:1876)(cid:2871)+(cid:885)(cid:1876)(cid:2870)=(cid:887)(cid:1876)+(cid:888) Solve develop and carry out a process for finding the solution or answer to a problem. Polynomial equation an equation in which one polynomial expression has the same mathematical value as another polynomial expression. Polynomial equation (cid:882)=(cid:1876)(cid:2871) (cid:886)(cid:1876) (cid:882)=(cid:884)(cid:1876)(cid:2871)+(cid:885)(cid:1876)(cid:2870) (cid:887)(cid:1876) (cid:888) (cid:882)=(cid:884)(cid:1876)(cid:2871)+(cid:885)(cid:1876)(cid:2870) (cid:887)(cid:1876) (cid:888) (cid:882)=(cid:4666)(cid:1876)+(cid:884)(cid:4667)(cid:4666)(cid:1876)+(cid:883)(cid:4667)(cid:4666)(cid:884)(cid:1876) (cid:885)(cid:4667) (x - intercepts) The zeros (x-intercepts) of a polynomial function, (cid:2207)=(cid:4666)(cid:2206)(cid:4667), are the solution(s) Example 1: solve the following for (cid:2206) using 2 different methods: (cid:2780)(cid:2206)(cid:2780) (cid:2779)(cid:2206)(cid:2779) (cid:2778)(cid:2779)(cid:2206)+(cid:2785)=(cid:2777). to the corresponding polynomial equation. Example 2: determine the roots of (cid:4666)(cid:2206)(cid:4667)= (cid:2206)(cid:2781)+(cid:2786)(cid:2206)(cid:2780)+(cid:2779)(cid:2778)(cid:2206)(cid:2779) (cid:2206) (cid:2780)(cid:2777). Polynomial equations can be solved using a variety of strategie, including: algebraically, graphically using a table of values, transformations, graphing technology. Only some polynomials can be solved by factoring, since not all polynomials are factorable. In these cases, graphing technology must be used. When solving problems using polynomial equations, it may be necessary to ignore solutions that are clearly unreasonable.
