Maths Question: Newtons Method of Approximation (1 Viewer)

[Sarah182]

I know how to use this method and all that, not a problem but Im curious how the best way to approach this question is:

Estimate the roots of equation x^4- 6x^2 +8x +1=0 by choosing appropriate approximations for the roots and using 1 application of Newtons Method

What is the best way to find "appropriate approximations" of the roots when they dont give a starting point??

 

[FOB all the way]

is this a past hsc question, what year?

 

[Sarah182]

Nope its just a challenge question out of my Year 12 maths in focus textbook.

 

[FOB all the way]

i would differentiate it and then use the formular to find x round it to 1 or 2 decimal place and use that as your approximation, maybe test the two answers from the formular to see which one is closer to the root before using it

 

[FOB all the way]

do you need the solution typed up?

 

[Sarah182]

Nope that makes sense to me
Thanks
I'll see how I go.

 

[jaychouf4n]

lol i was gonna suggest plugging random numbers into the calculator and if they got to 1 then that was an approximation.