A contradiction can be defined as a statement that is necessarily false. As you study mathematics, e

A contradiction can be defined as a statement that is necessarily false. As you study mathematics, especially logic, you will examine contradictory statements.Follow the directions outlined in the project guide. For this assignment you will be given three statements about polynomials. Two of the statements will agree with each other, while one of the statements will contradict the other two. It will be up to you to identify the contradictory statement and explain how it can be changed so that it is agrees with the other two statements.For information on how this assignment will be graded, please view the grading rubric.Assignment: Roots of Polynomial FunctionsPart 1 – Identifying the Contradictory StatementIn each of the following problems, three statements are given. Two of the statements agree witheach other. One of the statements contradicts the other two. Your task is to identify thecontradictory statement.For each problem:Identify the contradictory statement.Explain why the statement you chose contradicts each of the other two.Describe how the contradictory statement could be changed to make it agree with theother two statements.1.Statement 1:Statement 2:4 is a root of the polynomial f ( x )3Statement 3:2.Statement 1:Statement 2:Statement 3:f ( x ) x 7xf ( 4)30x37x6.6The polynomial f ( x )2x 3×225 x 12 has exactly three rational roots:1×3, x,x 42.According to the rational root theorem, the possible rational roots of the13, 1,, 2, 3, 4, 6,polynomial f ( x ) 2x 3 x 2 25 x 12 are225 2 1 25 1210By synthetic division:24512970© K12 Inc.12 .3.Statement 1:The graph of the function f ( x )Statement 2:f ( x ) 2x 3f (1) 6f (2)6Statement 3:x9x 22x 39x 2x 12 is:x 123is a rational root of the function f ( x )2© K12 Inc.2x 39x 2x 12 .Part 2 – Write Your Own ProblemNow it’s your turn to write a problem. For the problem you will:Write three statements about roots of polynomials. Two of the statements should agreewith each other. The third statement should contradict the other two.Identify the contradictory statement.Write at least two sentences to explain why the third statement is contradictory.Write at least two sentences to explain how the contradictory statement could be fixed tomake it agree with the other two.© K12 Inc.

 

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