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

The questioner wants us to list all possible roots by applying the Rational Roots theorem

factors of constant term (-20) = +/- 1, +/-2, +/-5, +/-10, +/-20 WE call these factors p.

factors of leading coefficient (2) = +/- 1, +/-2 (call these q)

then possible roots are p/q = +/-1/1, +/- 1/2 , +/- 5/1 , +/- 5/2 and so on.

Answer 2

The possible rational roots are given by the ratio of the constant term to the leading coefficient. That is $\pm$1/1, $\pm$1/2,  $\pm$1/5,  $\pm$1/10,  $\pm$1/20, and so on and this can be determined by using the arithmetic operations.

Given :

Polynomial Equation -- $2x^3+5x^2-8x-20=0$

The following steps can be used in order to determine the rational roots of the given polynomial equation:

Step 1 - Write the given polynomial equation.

$2x^3+5x^2-8x-20=0$

Step 2 - The coefficient of $x^3$ is 2. So the factors of 2 are $\pm$1, $\pm$2.

Step 3 - The constant term of the given polynomial is -20 and the factors of the constant term are  $\pm$1,  $\pm$2,  $\pm$5,  $\pm$10,  $\pm$20.

Step 4 - The rational roots are given by the ratio of the constant term to the leading coefficient. That is,

$\pm$1/1, $\pm$1/2,  $\pm$1/5,  $\pm$1/10,  $\pm$1/20, and so on.

For more information, refer to the link given below:

https://brainly.com/question/12254880