Ruffini-Horner Method/Examples
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Examples of Use of the Ruffini-Horner method
Arbitrary Example
Consider the polynomial equation:
- $\map f x = x^2 - x - 1 = 0$
We have that:
\(\ds \map f 1\) | \(=\) | \(\ds -1\) | ||||||||||||
\(\ds \map f 2\) | \(=\) | \(\ds 1\) |
so we observe there is a root between $x = 1$ and $x = 2$.
Then:
\(\ds \map {f_1} x\) | \(=\) | \(\ds \map f {x - 1}\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds \paren {x - 1}^2 - \paren {x - 1} - 1\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds x^2 - 3 x + 1\) |
We then identify a root between $x = 0.6$ and $x = 0.7$.
This leads to calculating:
- $\map {f_2} x = \map {f_1} {x - 0.6}$
Hence and so, until the required accuracy is achieved.