Use the Rational Zero Theorem to list all possible rational zeros for the given function. f(x) = - 3x4 - 20x3 +7x2 - 20x+ 6 ...

Algebra and Trigonometry (6th Edition)
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Author:Robert F. Blitzer
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ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Rational zero theorem

Use the Rational Zero Theorem to list all possible rational zeros for the given function.
f(x) = - 3x4 - 20x³ + 7x2 – 20x + 6
Choose the answer below that lists all possible rational zeros.
OA.
11
- 1,1, - 2,2, – 3,3, – 6,6, –
2'2
1 1
11
2 2
3 3
6'6
3'3
3'3
2'2
О в.
1 1
1 1
1 1
- 1,1, - 2,2, – 3,3, – 6,6, –
2'2
3'3
6'6
OC.
3 3
1 1
- 1,1, - 3,3, –
2'2
11
1 1
6'6
3'3
2'2
O D.
11
- 1,1, - 2,2, – 3,3, – 6,6, –
3'3
2 2
3'3
M IN
Transcribed Image Text:Use the Rational Zero Theorem to list all possible rational zeros for the given function. f(x) = - 3x4 - 20x³ + 7x2 – 20x + 6 Choose the answer below that lists all possible rational zeros. OA. 11 - 1,1, - 2,2, – 3,3, – 6,6, – 2'2 1 1 11 2 2 3 3 6'6 3'3 3'3 2'2 О в. 1 1 1 1 1 1 - 1,1, - 2,2, – 3,3, – 6,6, – 2'2 3'3 6'6 OC. 3 3 1 1 - 1,1, - 3,3, – 2'2 11 1 1 6'6 3'3 2'2 O D. 11 - 1,1, - 2,2, – 3,3, – 6,6, – 3'3 2 2 3'3 M IN
Expert Solution
Step 1

By rational zero theorem

possible rational roots=factors of constant termfactors of leading coefficientpossible rational roots=factors of 6factors of 3                                    =+1,-1,+2,-2,+3,-3,+6,-6+1,-1,+3,-3                                     =-1,1,-2,2,-3,-3,-6,6,-13,13,-23,23

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