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