Question

Answer the following questions about the equation below. x^3 - 14x - 8 = 0 (a) List all rational roots that are possible according to the Rational Zero Theorem. A. ± 8 B. ± 1 C. -1, -2, -4, -8 D. ± 1, ± 2, ± 4, ± 8 (b) Use synthetic division to test several possible rational roots in order to identify one actual root. One rational root of the given equation is [ ]. (Simplify your answer.) (c) Use the root from part (b) to solve the equation. The solution set is {[ ]}. (Simplify your answer. Type an exact answer, using radicals as needed. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.)

          Answer the following questions about the equation below.
x^3 - 14x - 8 = 0
(a) List all rational roots that are possible according to the Rational Zero Theorem.
A. ± 8
B. ± 1
C. -1, -2, -4, -8
D. ± 1, ± 2, ± 4, ± 8
(b) Use synthetic division to test several possible rational roots in order to identify one actual root.
One rational root of the given equation is [ ].
(Simplify your answer.)
(c) Use the root from part (b) to solve the equation.
The solution set is {[ ]}.
(Simplify your answer. Type an exact answer, using radicals as needed. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.)

Show more…

$Answer the following questions about the equation below. x^3 - 14x - 8 = 0 (a) List all rational roots that are possible according to the Rational Zero Theorem. A. ± 8 B. ± 1 C. -1, -2, -4, -8 D. ± 1, ± 2, ± 4, ± 8 (b) Use synthetic division to test several possible rational roots in order to identify one actual root. One rational root of the given equation is [ ]. (Simplify your answer.) (c) Use the root from part (b) to solve the equation. The solution set is [ ]. (Simplify your answer. Type an exact answer, using radicals as needed. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.)$

Added by Carmen C.

Precalculus with Limits

Ron Larson 2nd Edition

Instant Answer

Solved by Expert Julie Silva

01/16/2022

Step 1

Step 1:** List all rational roots possible according to the Rational Zero Theorem: 48, 41, -1, -2, -4, -41, 42, 4, 8 ** Show more…

Show all steps

lock

Thanks for your feedback!

Play audio

Feedback

Powered by NumerAI

Julie Silva and 54 other subject Precalculus educators are ready to help you.

Ask a new question

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Recommended Videos

Recommended Textbooks

Transcript

00:01 So in this problem, we're given this equation x to the third minus 14x minus 8.

00:04 In part a, the first thing we want to do is we want to use the rational zeros theorem to find the list of all of our rational zeros.

00:12 Well, to do this, what we need to do is we're going to take the factors of our constant term, which is negative 8, and we divide that by the factors of our leading coefficient, which is 1.

00:21 Well, the nice thing, because it's the factors of 1, that part actually won't cancel.

00:26 So really, we just need our factors in negative 8, which we plus or minus 1, plus and minus 2, plus and minus 4, and plus and minus 8.

00:34 So if you're looking at your list, in this particular case, the answer would be choice d.

00:38 So that's the answer to part a.

00:40 Now, in part b, what they've said is to use synthetic division to test some of these rational zeros to figure out which one is, in fact, in actual room.

00:49 So essentially, you could pick any number that you want.

00:51 So in this case, i'm going to use four.

00:53 So if i take four, that's going to go in our little half box, then i'm going to down our coefficient for each term.

00:59 Now keep in mind you're missing your x -square term, so you have to put the 0 in its place.

01:03 So you'll have 1 -0 -negative -14 as negative 8.

01:07 Then i'm going to leave a line in the space and bring down our 1.

01:10 Then we're going to multiply 1 by 4, which is 4, and then we add 0 plus 4 is 4.

01:15 And we'll continue this process.

01:17 4 times 4 is 16, negative 14 plus 16 is equal to 2, 2 times 4 is 8, and negative 8 plus 8 is 0.

01:24 Perfect.

01:25 So now what we've found is that 4 is one of our roots.

01:29 So that's the answer to the part b.

01:31 Now lastly, part c, they want us to use this result to find the remaining roots...

Ace is your personal tutor. It breaks down any question with clear steps so you can learn.

Start Using Ace

Continue solving this problem

Create a free account to:

View full step-by-step solution
Ask follow-up questions with Ace AI
Save progress and study later