Answer:
4.3 to 1 decimal place.
Step-by-step explanation:
x^3 - 5x - 59 = 0
Try x = 4.1:
f(4.1) = (4.1)^3 - 5(4.1) - 59 = -10.579
Try: 4.2:
f(4.2) = 4.2^3 - 5(4.2) - 59 = -5.912, Try x = 4.3:
f(4.3) = -0.993 (getting closer to 0!!)
f(4.4) = 4.184
NOTICE - there is a change of sign in the result so the root lies between 4.3 and 4.4.
Try x = 4.35:
f(4.35) = 1.563 so it looks like the root is closer to 4.3 than 4.4 because 1.563 is closer to zero than 4.184.
Just to double check let's calculate x = 4.32:
f(4.32) = 0.0216 - which is very close to zero.
So the answer is 4.3 to 1 decimal place.
(I've checked it out on my calculator - the root is 4.31958).
