Question

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

Answer 1

Its Option 1

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.

Answer 2

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

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