Question

I want to find the roots of x^3+2x^2-3x-1=0 using bisection method. But Im not sure how to select the initial approximation. Can you tell me how select a suitable initial approximation to this?

Answer 1

i wl tell u d trick

Answer 2

ok. tl me.. my buk menyons something called taylor method. But i hav no ida abt it.

Answer 3

mentions

Answer 4

frst select the interval where sign of the equation changes

Answer 5

exactly you have to choose smallest interval of two points say a and b such that f(a)<0 and f(b)>0

Answer 6

absolutely right

Answer 7

so that interval is (a,b)

Answer 8

can u tell me how to select the intervals?

Answer 9

first method is hit n trial..................

Answer 10

can i differentiate and find it?

Answer 11

gd there u cn find the points where slope is zero

Answer 12

by differntiating u gt x= 0.58 n - 2.58

Answer 13

yep. so what should i do after that?

Answer 14

then take points nearer to one point u wl see sign of equation changes similarly repeat for other point that u hav find after differntiation....

Answer 15

but does the sign of the eqn changes on a occassion like this?

Answer 16

i didn't get wat r u saying????

Answer 17

You said I should select tha interval where the sign of the equation changes.

Answer 18

w8 i m clearing

Answer 19

first put x = 0 in the original cubic equation tl me wat u get ?

Answer 20

asap

Answer 21

1

Answer 22

dear it's negative keep all the expression on the left while putting so u gt -1

Answer 23

then put x = 1 u wl get -1 again .........till now sign of the function is negative kk

Answer 24

yep.. i got it

Answer 25

nw put x = 2 u wl gt 9 which is positive so ur initial approximation is (1,2)

Answer 26

hope u gt it dear NEO

Answer 27

THEN APPLY BISECTION

Answer 28

Okey.. i gt it now. so is that the only way.. ?

Answer 29

yup dear n thanks fr awarding me the medal

Answer 30

:)

Answer 31

so I hav to apply the same method for an eqn like \[3x-e ^{x}=0\]

Answer 32

u can dear........

Answer 33

here interval is wat tl me asap?

Answer 34

wait a min

Answer 35

i wl

Answer 36

is it (1,2) ?

Answer 37

w8

Answer 38

by putting 1 u get 1.74 n fr x = 0 u gt -1 so changes here first interval is (0,1)

Answer 39

oh yes.. i hav missed the -sign when calculating
and i think 1 gives 0.28..... (3-e)

Answer 40

gt it dear