Question

Roots of equation help. *question attached below* Will give medal.

Answer 1

So, I have already completed part a and b for this question, but I have a little trouble understanding what the question is asking for in part c, when it says "approximation to the smaller of the positive root. Can someone explain what this statement means? I know how to do linear interpolation, I'm just a bit confused as to what part c is asking.

For the intervals, I got (-2,-1), (0,1) and (1,2)

Answer 2

I got those same intervals.

Answer 3

Do you want to check the chart in part a or is that okay?

I understand that part c is your primary interest but wanted to be sure the first two parts are okay.

Answer 4

Sure, I got these values for the table for f(x):
-1, 3, 1, -1, 3

Answer 5

Your smaller positive root lies between 0 and 1.

Answer 6

So, that means that I need to apply linear interpolation once with that interval?

Answer 7

I got what you did on the chart so that's fine.

I have done linear interpolation and remember that there is a proportion to set up.

Let me think.

Answer 8

On the chart (0,1) nd (1,-1) are consecutive points. Because the y-values jump fom 1 to -1, a root lies between those two points. That is because to get from 1 to -1, you have to pass through 0.