Question

Which of the following represents the set of possible rational roots for the

polynomial shown below?
2x3 + 5x2 – 8x – 20 = 0

Answer 1

• D

Step-by-step explanation:

Simplify the given equation by dividing all terms by 2:

• x³ + 2.5x² - 4x - 10 = 0
• x²(x + 2.5) - 4(x + 2.5) = 0
• (x + 2.5)(x² - 4) = 0
• (x + 2.5)(x + 2)(x -2) = 0

Roots are:

• - 2.5, -2, 2

Correct choice is D

Answer 2

Answer: Choice D

The plus/minus of the following: 1/2, 1, 2, 5/2, 4, 5, 10, 20

========================================================

Step-by-step explanation:

Refer to the rational root theorem. To find the possible rational roots, we divide the factors of the last term 20 over the factors of the first coefficient 2.

• Factors of 20 are: 1,2,4,5,10,20
• Factors of 2 are: 1,2

Dividing those said factors leads us to the list in choice D. We include the positive and negative versions of each result. For example, divide 10 over 2 to get 10/2 = 5 as one possible root (which leads to -5 as well).

A table like the one shown below might be handy to keep track of all the terms.