g(x) = x 5 5x 6 a. Show that g(x) = 0 has a root,

Question:

g(x) = x⁵ − 5x − 6

a. Show that g(x) = 0 has a root, α, between x = 1 and x = 2.

b. Show that the equation g(x) = 0 can be written as x = (px + q)^1/r, where p, q and r are integers to be found.

The iterative formula

is used to find an approximate value for α.

c. Calculate the values of x₁, x₂ and x₃ to 4 decimal places.

d. By choosing a suitable interval, show that α = 1.708 is correct to 3 decimal places.

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Pearson Edexcel A Level Mathematics Pure Mathematics Year 2

ISBN: 9781292183404

1st Edition

Authors: Greg Attwood, Jack Barraclough, Ian Bettison, David Goldberg, Alistair Macpherson, Joe Petran

See More Books

Question Posted: Aug 17, 2023 03:07 AM

See More Questions

A comparison of reaction times (in seconds) for two different stimuli in a psychological word-association experiment produced the following results when applied to a random sample of 16 people: Do...
The following table lists the annual amounts of glass cullet produced by Kimble Glass Works Inc. for 2013 through 2017. Determine the least squares trend equation. Estimate the amount of scrap for...
Find an expression for f 1 (x) for each of the following functions. a. f(x) = 5x 8 for x b. f(x) = x 2 + 3 x x + for x , x 0 c. f(x) = (x 5) 2 + 3 for x , x 5 d. e. f. f(x) = (x 2) 3 1 for...
Briefly explain the differences between copyrights and patents.
Matuseski Corporation is preparing its cash budget for October. The budgeted beginning cash balance is $17,000. Budgeted cash receipts total $187,000 and budgeted cash disbursements total $177,000....
What is an Achilles' heel and why would a certain assumption about lead times be considered the Achilles' heel of MRP?
What is a process? Why are processes important in project management? AppendixLO1
Air France-KLM (AF), a Franco-Dutch company, prepares its financial statements according to International Financial Reporting Standards. AF's financial statements and disclosure notes for the year...
Journal all transactions in Part One using the line designators in Part One , etc. ) in place of dates. Using the chart of accounts, open ledger accounts in " T " account format and post journals to...
f(x) = x 3 + 5x 2 2 a. Show that f(x) = 0 can be written as: b. Starting with x 0 = 10, use the iterative formula in part a (i) to find a root of the equation f(x) = 0. Round your answer to 3...
f(x) = sin x ln x , x > 0, where x is in radians. a. Show that f(x) = 0 has a root, , in the interval [2.2, 2.3]. b. By considering a change of sign of f(x) in a suitable interval, verify that =...
Compare and contrast the following two statements. Are they concerned with achieving eco-efficiency, eco-effectiveness or both? 1 Businesses should sack the unproductive kilowatt-hours, tonnes and...
Case study: Sun City - improving operations performance to enhance guest experience 1. Describe how Sun City implements the five operations performance objectives or principles. 2. Using your...
What recommendations do you have to increase the likelihood of success? E.g., how would you reduce the likelihood of having to go back to A4? How would you reduce the impact of having to go back to...
Problem 4 An electrically heated, square plate (0.4mx 0.4 mx0.005 m) is suspended in air of temperature Too = 20C. Find the electrical power needed to maintain the plate at T=95C if the plate is (a)...
Number of units Unit Cost Sales Beginning inventory 800 $50 Purchased 600 $52 Sold 400 $80 Sold 350 $90 Ending inventory 650 In the table below, calculate the dollar value for the period for each of...
10. Dr. D went to MGM Springfield casino while the class was taking their midterm exam. He played a Konami machine entitled 88 Fortunes. A slot attendant accidently left the slot manual next to the...
You have a sample of water and are able to control temperature and pressure arbitrarily. (a) Using Fig. 13-22, describe the phase changes you would see if you started at a temperature of 85°C, a...
l ask this second time correnct answer is 38,01 can we look pls Consider a non-conducting rod of length 8.8 m having a uniform charge density 4.5 nC/m. Find the electric potential at P, a...
There are no universally accepted definitions of the ages of Millennials and Generation Xers; the consensus is that the former are Americans born between 1984 and 2000 and the latter are Americans...
Many critics of television claim that there is too much violence and that it has a negative effect on society. There may also be a negative effect on advertisers. To examine this issue, researchers...
Refer to Exercise 6.28. a. Compute P(A 1 or A 2 ). b. Compute P(A 2 or B 2 ). c. Compute P(A 3 or B 1 ). In exercise 6.28 Suppose we have the following joint probabilities. A, B, B2 Az A2 .20 .25 .10...
Comfort Golf Products is considering whether to upgrade its equipment Managers are considering two options. Equipment manufactured by Stenback Inc. costs $1,000,000 and will last five years and have...
Weaver Corporation had the following stock issued and outstanding at January 1, Year 1: 71,000 shares of $10 par common stock. 8,500 shares of $60 par, 6 percent, noncumulative preferred stock. On...
Read the following case and then answer questions On 1 January 2016 a company purchased a machine at a cost of $3,000. Its useful life is estimated to be 10 years and then it has a residual value of...

g(x) = x 5 5x 6 a. Show that g(x) = 0 has a root,

Question:

Xn+1 = (px +q) ½ , xo = 1

Step by Step Answer:

a g1 10 0 g2 16 0 The sign change implies there ...View the full answer

Pearson Edexcel A Level Mathematics Pure Mathematics Year 2

Students also viewed these Mathematics questions