Question

Describe Newton's Method and its purpose

Answer 1

used for approximating the root of a polynomial.

the roots of a quadratic can be found be factorising and solving, completing the square or the general quadratic formula.

For higher order polynomials it is more difficult to find the roots...

hence Newton's method.

given a polynomial P(x)

if P(a) > 0 and P(b)< 0 then a zero exists between a and b

Newton"s method requires the 1st derivative of the polynomial

so the a root is between a and b make a guess at the root... possibly \[x _{0}=\frac{(a +b)}{2}\]

then the formula is

\[x _{1} = x _{0} - \frac{f(x _{0})}{f'(x _{0})}\]

the approximation method can be repeated until a value is obtained.
then the approximation

Answer 2

Thank you!! Very helpful! I know what the answer is just couldn't put it into a shorter answer. Once again thank you