HSC Polynomial question (1 Viewer)

[Aysce]

Okay, i know polynomials is one of the easiest topics for HSC 3u, but i'm new to this and kinda confused. Okay it says,

Find the approximation of a root of the function f(x)= x^7-2 that lies between x=1 and x=2 by halving the interval once.

So i halved 1+2, and got 3/2. When i subbed it in, I received an answer of 15.09? The answer is x = 1 (rounded) I checked over and did it the same way with the other questions ><

 

[MATHSCAPE]

f(x) = x^7 - 2
f(1) = -1
f(2) = 126
you know the root lies between x=1 and x=2 but you can narrow that interval further if you half it.
f(1.5) = 15.085..
now you know the root lies between x=1 and x=1.5
round it to the nearest whole number, 1.

 

[D94]

Okay, i know polynomials is one of the easiest topics for HSC 3u, but i'm new to this and kinda confused. Okay it says,

Find the approximation of a root of the function f(x)= x^7-2 that lies between x=1 and x=2 by halving the interval once.

So i halved 1+2, and got 3/2. When i subbed it in, I received an answer of 15.09? The answer is x = 1 (rounded) I checked over and did it the same way with the other questions ><

Yeah, that's right. We know f(1) = -1, and f(3/2) = 15.09. So is the root closer to 1 or 3/2? It's evidently closer to 1.

 

[Aysce]

Okay thanks a lot guys

 

[Aysce]

Btw, do you guys know anyone that has more of these questions, if so can you please say so. Cheers

 

[slyhunter]

Don't you have a textbook?

 

[Aysce]

I've done the exercises so yeah, just need a little more, not completely confident yet

 

[barbernator]

Btw, do you guys know anyone that has more of these questions, if so can you please say so. Cheers

(vi) (1) Show that there is a solution to the equation x=e^-x^2
between
x = 0.6 and x = 0.7
(2) By halving the interval, find the solution correct to one decimal
place.

thats another from the 2010 HSC paper

 

[MATHSCAPE]

Btw, do you guys know anyone that has more of these questions, if so can you please say so. Cheers

http://www.boredofstudies.org/download.php?id=9242
http://www.boredofstudies.org/download.php?id=9243
HSC and CSSA questions.