URGENT: Halving the interval (1 Viewer)

[TimeGoesTooFast]

Okay, so even after consulting the head teacher at school, I'm still confused...

Question: let f(x)=x^3+5x^2+17x-10. function has one real root.

i) show that root lies between 0 and 2.
ii) use one application of halving the interval method to find smaller interval containing the root.
Note: done these two

iii) which end of the smaller interval found in part ii) is closer to the root? justify your answer

When you halve the interval, f(0.5)=-0.125. I don't understand why the answer says the root lies closer to 1, not 0. Isn't it closer to 0 though?

 

[SharkeyBoy]

f(2) = 52 , f(0) = -10
f(1) = 13 (replace f(2) with f(1))
f(0) is closer to 0 than f(1), so it should be f(0) i think

 

[TimeGoesTooFast]

Okay that's what I thought but answers say otherwise...maybe I'll just ask again LOL. Thanks Sharkey ^.^

 

[SharkeyBoy]

no worries

 

[TimeGoesTooFast]

Actually, nvm didn't realise question said interval. So it's closer to 1 since the root lies with the INTERVAL 0.5 and 1. Thanks again haha.

 

[Capt Rifle]

lol just a heads up, there are barely halving interval questions, i reckon 90% of the time newton method will be asked in the hsc