4. A multiple root of a polynomial is a root that occurs more than once and corresponds to a point where a function is tangent to the x axis for example the polynomial: The factor occurs twice, so it is a multiple root. Since it occurs twice, also called a double root. Source: http://www.lifeisastoryproblem.org/vocab/es/m/multipleroot.html
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7. The three initial values are denoted as xk, xk-1 y xk-2. The parabola passes through the points: (xk, f(xk)), (xk-1, f(xk-1)) y (xk-2, f(xk-2)), if it is written in the form of Newton, then: where [xk, xk-1] y f[xk, xk-1, xk-2] denote subtraction divided. This can be written as: Where The next iteration is given by the root that gives the equation y = 0.
8. BAIRSTOW METHOD Bairstow's method is an iterative method, based on the method of Müller and Newton Raphson. Given a polinoniofn(x) are two factors, a quadratic polynomial f2(x) = x2 – rx – s y fn-2(x). The general procedure for the Bairstow method is: Since fn(x) and r0 and s0 Using the method of NR calculate f2(x) = x2 – r0x – s0 and fn-2(x) , such that the residue of fn(x)/ f2(x) is zero. Determine the roots f2(x), using the general formula. It is estimated fn-2(x)= fn(x)/ f2(x). We fn(x)= fn-2(x) If the degree of the polynomial is greater than three back to step 2If we do not finish
10. To calculate the result of a complex number, or N-ESIMA root, we use a variant of Euler, this formula states that every complex number has exactly n complex roots.Where: k = 0,1,2 ,...... n-1 that is generating each of the roots. www.katjaas.nl/rootsofunity/rootsofunity.html
11. EXAMPLE: calculate the square root of: first polar graph mode is solved in polar form first and then being able to replace in the formula above written. Im this is the polar form now follows the substitution in the Euler formula .. Re Re
