Question

okay i just need process for this
to find root using bisection method.
x^2-4x-10=0

Answer 1

\[\Delta=b^2-4ac=16-4(-10)(1)=16+40=56\\
x=\frac{-b\pm\sqrt{\Delta}}{2a}
\]

Answer 2

no no no
bisection method

Answer 3

ooh
k
1.
find [a,b] where f(a) and f(b) will have opposite signs

Answer 4

@Eskijoe no

Answer 5

2. c=(a+b)/2
3. find f(c)
4. see if [a,c] or [c,b] have opposite signs
5. proceed with step 2 with the new interval

Answer 6

@electrokid how do i find that? f(a) f(b) with opposite signs

Answer 7

@Eskijoe why not? the discriminant is +ve
it has real roots

Answer 8

@aajugdar if the interval is not provided, start with a +ve x and -ve x by trial-error

Answer 9

oh okay
got ya

Answer 10

lets take a=0. f(a)=-10<0
now, we start our hunt for b such that f(b)>0

Answer 11

hint:
x(x-4)=10

Answer 12

oh sorry misread -10 as 10, lol

Answer 13

here
f(0) = -10
f(-2) = 2

Answer 14

we need x(x-4)>10

Answer 15

b=6 should satisfy

Answer 16

10?
you said opposite signs ryt

Answer 17

iter#1 [a,b]=[0,6] -> [-,+]
c = 3 f(c)=9-12-10<0
iter#2 [a,b]=[3,6] -> [-,+]
c=(3+6)/2=4.5 f(c)....
and continue till you get f(c) close to 0 to your tolerance value

Answer 18

f(0) = -10
and f(2)= 2?

Answer 19

wait wait

Answer 20

f(-2) i meant

Answer 21

remember, interval [a,b], a<b

Answer 22

yes you can have [-2,0]
its perfectly fine

Answer 23

so i can say root lies btwn 0 and -2?

Answer 24

remember.. this is a quadratic function and has 2 distinct roots.
we just found the two intervals where they are

Answer 25

i see

Answer 26

-2+0/2 = -1
f(-1) = -5
so its like (-2,-1) (-1,0) now

Answer 27

how do i proceed from here

Answer 28

no no
f(-2)>0 f(-1)<0 f(0)<0
so, opposite signs..
new interval would be [-2,-1]

Answer 29

oh
got ya

Answer 30

you have just narrowed down your domain.
we keep narrowing down and get closer to the thief based on the sign clues

Answer 31

that is bisection method, no hint how much closer
in regula falsi, we use slope of "secant" as clue.. a linear hint of closeness
in Newton raphson, we use slope of "tangent" as clue... quadratic hint of closeness

Answer 32

you can do this really quick in excel too..

Answer 33

thanks :) got it