1. ## halving the interval

f(x) = x^3 + 5x^2 + 17x - 10.
The equation f(x) = 0 has only one real root.

i. Show the root lies between 0 and 2

ii. use one application of 'halving the interval' to find a smaller interval

iii. Which end of the smaller interval found in ii. is closer to the root? Why?

for i. i got
P(0) = -10 -neg
P(2) = 52 -pos
therefore the root lies between 0 and 2

ii. P(1) = 13 -pos
therefore the root lies between 0 and 1

are these right??
how do you do iii.?

2. Originally Posted by deej813
f(x) = x^3 + 5x^2 + 17x - 10.
The equation f(x) = 0 has only one real root.

i. Show the root lies between 0 and 2

ii. use one application of 'halving the interval' to find a smaller interval

iii. Which end of the smaller interval found in ii. is closer to the root? Why?

for i. i got
P(0) = -10 -neg
P(2) = 52 -pos
therefore the root lies between 0 and 2

ii. P(1) = 13 -pos
therefore the root lies between 0 and 1

are these right??
how do you do iii.?
P(0.5)<0,so the root is greater than 0.5, then 1 is nearer..
i,ii are right.

3. ok thanks