Find the root of the problem - 2
Given the initial approximation of the root . Which of the listed numerical methods would you choose to solve the following equation:
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1 solution
The Newton Raphson method has the following form to calculate the successive approximations for root...
x n + 1 = x n − f ′ ( x n ) f ( x n )
In our problem we have the polynomial f ( x ) = 5 x 5 − 1 1 x 4 + 3 6 2 3 x 3 − 1 7 5 4 x 2 + 6 6 2 4 x + 7 6 8 4 8 5 8 taking the first derivative gives... f ′ ( x ) = x 4 − 4 4 x 3 + 6 2 3 x 2 − 3 5 0 8 x + 6 6 2 4 Now to find x 1 we must evaluate f ′ ( x 0 ) f ′ ( 9 ) = 0 Newton's method fails, hence we have to use bisection method. Analytical method is out of question as it is clearly mentioned that numerical method has to be used. Though bisection method takes more iterations it is the best method out of the given set of options. Hence, choice (a) is right.