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

## Question:

g(x) = x^{5} − 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 x_{1}, x_{2} and x_{3} to 4 decimal places.

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

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## Step by Step Answer:

**Related Book For**

## 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

**Question Details**

Chapter #

**10**Section: Mixed exercise

Problem: 4

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