Newton's approximation/halving method question (1 Viewer)

[physicss]

This is taken from the Maths in Focus 2 textbook in the polynomials section.

i) Sketch curve y=x^4 - 6x^2 + 8x +1

ii) Estimate the roots of the equation x^4 - 6x^2 + 8x +1=0 by choosing appropriate approximations for the roots and using 1 application of Newton's method.

iii) One of the roots is a poor estimation. Which one is it?

iv) By halving the interval twice, find the best estimate of this root.


I need help on how to do part iv) please, because I cannot get the right answer.

ANSWERS: ii) x=-0.17,x=-3.21 iii) x=-3.21 iv) x=-3

 

[random-1006]

This is taken from the Maths in Focus 2 textbook in the polynomials section.

i) Sketch curve y=x^4 - 6x^2 + 8x +1

ii) Estimate the roots of the equation x^4 - 6x^2 + 8x +1=0 by choosing appropriate approximations for the roots and using 1 application of Newton's method.

iii) One of the roots is a poor estimation. Which one is it?

iv) By halving the interval twice, find the best estimate of this root.


I need help on how to do part iv) please, because I cannot get the right answer.

ANSWERS: ii) x=-0.17,x=-3.21 iii) x=-3.21 iv) x=-3

lol, thought this question looked familiar.

you probably wont get the textbooks answer as they havent givent you an interval to go through, they are asking you to sort of "select your own interval". its a fairly stupid question, dont worry about it, as long as you know the basic technique

e.g. if p(1) = 1 and p(2) =-1, your first guess would be p(1.5 ) , if that were say p(1.5) = -0.5 then your next guess would be p ( (1 +1.5)/ 2)