i need help please

[clear remnant]

Hi can someone please tell me why did we chose f(a)×f(x2) and not f(x1)*f(x2)

[mortal slate]

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[lyric whale]

what's the difference

also provide context

that included sending the whole page/problem

[lyric whale]

ok

[clear remnant]

Sorry about that

Its bisection method

[wise gate]

oh this is the newtons method of finding the x intercept isnt it

[clear remnant]

Its actually bisection method

[wise gate]

oh ok

whats it used for ?

[lyric whale]

they chose a for the fun of it

and as f(a)*f(x1) < 0 as stated

[clear remnant]

We need to find the approximate root

[lyric whale]

they can now look for roots in [a, x1]

[clear remnant]

But why he didnt choose f(x1)*f(x2)

[lyric whale]

to maybe first confirm if there's root in [a, x1]

and then he showed that there are no roots in [a, x2]

this would man that roots are in (x2, x1]

[clear remnant]

How do i know if the root exist or not

[lyric whale]

they are narrowing down the search

[lyric whale]

in (x2, x1]?

by the fact that if f(a)f(b) < 0 the there's a root between a and b

[clear remnant]

I know who to find the new root i just dont get it why in all of the steps we said for example f(x2,f(x3) in step 4

[lyric whale]

mhn

as I said, they narrowed down the search!

[clear remnant]

I get this but my question is how do we know which one is f(c)*f(a)

[lyric whale]

you don't

it's trial and error

that's the point of numerical analysis

[clear remnant]

😭😭😭

[lyric whale]

you know here as you are finding the root to "x^2 - 2"

[clear remnant]

I just dont know how to choose the correct f(c)*f(a)

That is my problem😭

[lyric whale]

https://youtu.be/zkd6CLfNNe8?feature=shared

watch this

[lyric whale]

bro thats the whole point, it's a method to find roots via computers

you guess

[clear remnant]

We actually do this by hand😭

We have a practical exam and Theory exam

[lyric whale]

that's brutal

[clear remnant]

Im so SCARED I DONT KNOW WHAT TO DO😭😭😭😭😭

[lyric whale]

i mean

let's try a example

let's say we want to find a root to

$f(x) = x^2 - x - 1$

[obsidian moon]

Coffey

[lyric whale]

how'd YOU start @clear remnant

[clear remnant]

So i will see if it apply the conditions of bisection

Since its a polynomial function so that means it's continues so that means it apply the first condition

But for the second condition i need a root

[lyric whale]

yk what

[clear remnant]

U need to give me a root also

[lyric whale]

don't bother with the formalities

just find a root.

approximation.

let's say error is less than 10^-3

[clear remnant]

U have to give me an error and a root

[lyric whale]

nah you are going to FIND the root

atleast approximate it

[clear remnant]

I MEANT AN INTERVAL

I need an interval

[lyric whale]

start within [1,2]

[clear remnant]

Ok

[lyric whale]

can't you eyeball it

like it's clear it's [1,2]

right

[clear remnant]

So f(1)=-1,f(2))=1

[clear remnant]

For x1=a+b/h ,, 1+2/2=1.5 |x1-a|=|1.5-1|

[lyric whale]

keep going idk

tell me the root at last

[clear remnant]

0.5>10^-3

Find x2

[lyric whale]

man can't you use a programme

[clear remnant]

F(x1)=-0.25

So now i have problem

I dont which one should i use

[clear remnant]

No 😭😭

[lyric whale]

check all of em lol

[clear remnant]

That will take a super long time and i dont have that much time in exam😭😭😭

[lyric whale]

too bad

every time you literally only have 2 choices bro

if one [a, c] doesn't work in [a, b] b then [c, b] does