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.

Transcribed Image Text:

Xn+1 = (px +q) ½ , xo = 1