Question

Using synthetic division and perform two iterations of the Birge-Vieta method to find
the smallest positive root of the equation 0 3 3 3 2
4 3 2
x − x + x − x + = . Use the initial
approximation 5.0 x0 = .

Answer 1

Answer on Question #46678 – Math – Algorithms | Quantitative Methods

Using synthetic division and perform two iterations of the Birge-Vieta method to find the smallest positive root of the equation $x^4 - 3x^3 + 3x^2 - 3x + 2 = 0$. Use the initial approximation $p_0 = 0.5$.

Solution:

In the given task according to the condition, we have the initial approximation $p_0 = 0.5$. So we apply the synthetic division to our equation based on the above information.

Then the value of $p_1 = p_0 - \frac{b_4}{c_3} = 0.5 - \frac{0.9375}{-1.750} = 1.0356$

Now we substitute the find value of $p_1$ equal to 1.0356.

Then we can calculate the value of $p_2 = p_1 - \frac{b_4}{c_3} = 1.0356 - \frac{-0.0711}{-1.9960} = 0.99997875$

Finally we found the smallest positive root of the equation which is equal to 1.0

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