Polynomion Functions, Roots and Other Assigments

I include 2 assigments, each of them with several questions that need to be complete clear, full and correctly.Provide evary step and DO NOT OMIT any of them. SHOW THE WORK CLEARLYNO PLAGARISMEVERY QUESTION AND PART OF THE QUESTION NEED TO BE ANSWERED CORRECTLYThanks
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Assignment: Roots of Polynomial Functions
Part 1 ? Identifying the Contradictory Statement
In each of the following problems, three statements are given. Two of the statements agree with
each other. One of the statements contradicts the other two. Your task is to identify the
contradictory 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 the
other two statements.
1.
Statement 1:
Statement 2:
4 is a root of the polynomial f ( x )
3
Statement 3:
2.
Statement 1:
Statement 2:
Statement 3:
f ( x ) x 7x
f ( 4)
30
x3
7x
6.
6
The polynomial f ( x )
2x 3
x2
25 x 12 has exactly three rational roots:
1
x
3, x
,x 4
2
.
According to the rational root theorem, the possible rational roots of the
1
3
, 1,
, 2, 3, 4, 6,
polynomial f ( x ) 2x 3 x 2 25 x 12 are
2
2
5 2 1 25 12
By synthetic division:
2
10
45
12
9
7
0
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12 .
3.
Statement 1:
The graph of the function f ( x )
Statement 2:
f ( x ) 2x 3
f (1) 6
f (2)
6
Statement 3:
x
9x 2
2x 3
9x 2
x 12 is:
x 12
3
is a rational root of the function f ( x )
2
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2x 3
9x 2
x 12 .
Part 2 ? Write Your Own Problem
Now 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 agree
with 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 to
make it agree with the other two.
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