Maths C3 - Numerical Methods.. Question Help??

Ok so as embarrassing as this sounds I'm stuck on Example 1 from the Numerical Methods chapter of the Edexcel C3 Modular Maths Textbook...



How am I meant to draw the cubic graph if I can't even get it to factorise in order to work out the points where it intercepts the x-axis??

I find that the book hasn't really described this topic very well. Am I missing something?


Also I think I will be posting other problems that I get stuck on in this chapter to this same thread instead of spamming TSR with new threads like I usually do :P

Not embarrassing at all, I think this is one of the few places where the Edexcel textbook fails.

I don't think you're expected to draw that - it most likely sufficies to find f(2) and f(3) and show that there
s a change of sign.

Oh right I see. I was wondering that. I've actually wasted like the last hour thinking whether I'm just being stupid and can't work it out

Do you understand why showing the signs of f(2) and f(3) are different is enough to show that the function crosses the x-axis somewhere between there?

Yes I think so. It's because it shows that f(2) and f(3) are leaning close to y=0 as f(2) is slightly less than y=0 and that f(3) is slightly more than y=0.

Am I right?

Yeah, the signs being different means that the curve is under the x-axis at f(2) (say f(2) is negative) and above the x-axis at f(3), so it must have crossed the x-axis somewhere in between there.

Is it just me or is iteration a very "trial and error" based method? It seems very monotonous to me. :/

Is it just me or is iteration a very "trial and error" based method? It seems very monotonous to me. :/

Trial and error is much more random. Iteration always leads you straight to a very good approximation of the answer if you iterate enough times depending on your starting point.

Interval bisection method to find a more accurate interval of something, such as a root to an equation, is much more trial and error based than iteration.

Yeah, the signs being different means that the curve is under the x-axis at f(2) (say f(2) is negative) and above the x-axis at f(3), so it must have crossed the x-axis somewhere in between there.