Determine a root of the polynomial function using Muller’s Method...

in Other Math Topics by

Your answer

Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:
To avoid this verification in future, please log in or register.

1 Answer

This is likely to be a lengthy solution so I may need to abbreviate some of the details. But first we need some preliminaries. Here is a table and a graph. f(x) is shown in red. The blue curve is a parabola attempting to match the shape of the curve using three points near to a zero. The roots, or zeroes, are the 4 points of intersection of the red curve and the x-axis.

 

 

 

 

Now to find the parabola’s equation. There are various ways to do this but I’ll use simultaneous equations.

g₁(x)=ax²+bx+c. To find a, b, c using x₀=-15, x₁=-10, x₂=-5.

(1) 40.2926=225a-15b+c

(2) -35.6704=100a-10b+c

(3) -12.2184=25a-5b+c

(1)-(2): 75.963=125a-5b-151.926=-250a+10b

(1)-(3): 52.511=200a-10b

Adding the last two equations: -99.415=-50a, a=1.9883.

From this b=34.5149, c=110.6486.

g(x)=1.9883x²+34.5149x+110.6486 (blue curve).

More to follow...

by Top Rated User (1.2m points)

Related questions

1 answer
asked Feb 18, 2021 in Other Math Topics by anonymous | 1.2k views
1 answer
asked Feb 18, 2021 in Other Math Topics by anonymous | 1.0k views
1 answer
asked Feb 18, 2021 in Other Math Topics by anonymous | 980 views
1 answer
asked Feb 18, 2021 in Other Math Topics by anonymous | 689 views
1 answer
asked Feb 18, 2021 in Other Math Topics by anonymous | 510 views
1 answer
asked Feb 18, 2021 in Other Math Topics by anonymous | 894 views
1 answer
asked Feb 18, 2021 in Other Math Topics by anonymous | 1.6k views
Welcome to MathHomeworkAnswers.org, where students, teachers and math enthusiasts can ask and answer any math question. Get help and answers to any math problem including algebra, trigonometry, geometry, calculus, trigonometry, fractions, solving expression, simplifying expressions and more. Get answers to math questions. Help is always 100% free!
87,515 questions
100,352 answers
2,420 comments
767,977 users