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Feliz [49]
3 years ago
14

Which of the following represents the set of possible rational roots for the polynomial shown below 2x^3+5x^2-8x-20=0

Mathematics
2 answers:
kvasek [131]3 years ago
8 0

Answer:

± 1/2,±1, ±2,± 5/2, ±4 ,±5 , ±10, ± 20

Step-by-step explanation:

We can use the rational root theorem to find all the possible roots

2x^3+5x^2-8x-20=0  

Let the constant term  be called p and the leading term be called q.  Then the possible roots are the positive and negative roots of the factors of p/q

p = 20

q = 2

Factors of p: 1,2,4,5,10,20

Factors of q: 1,2

Possible roots

    1 ,2,4,5,10,20

±   --------------------------------------------------------

      1,2

So we get

±1, ±2, ±4 ,±5 , ±10 ± 20 ± 1/2± 2/2,±4/2,± 5/2,± 10/2,± 20/2

Simplifying

±1, ±2, ±4 ,±5 , ±10, ± 20, ± 1/2,± 1,±2,± 5/2,± 5,± 10

Eliminating repeats

±1, ±2, ±4 ,±5 , ±10, ± 20 ,± 1/2,± 5/2

Putting them in numerical order

± 1/2,±1, ±2,± 5/2, ±4 ,±5 , ±10, ± 20

Masteriza [31]3 years ago
3 0

Answer:

Its Option 1

Step-by-step explanation:

The possible rational roots will have a numerator that divides 20 (the last number) and a denominator that divides 2 (the coefficient of x^3).

For example 20/2, 10/2 and -1/2  =  10, 5 and -1/2.

The correct answer is the first option.

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svlad2 [7]

Answer:

The answer to your question is below

Step-by-step explanation:

5)                                2x² -7x + 34

                       x + 5   2x³ + 3x² - x + 1

                                 -2x³ -10x²

                                   0   - 7x² - x

                                        +7x² +35x

                                           0   +34x + 1

                                                 -34x - 170

                                                    0   - 160

Quotient = 2x² - 7x + 34

Remainder = -160

6)                                       2x² - 3x  + 1

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                                                        - 3x - 1

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Quotient = 2x² - 3x + 1

Remainder = 1

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2 years ago
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