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Newton-Raphson method is used to find the roots of the equation, x3 + 2x2 + 3x – 1 = 0. If the initial guess is x0 = 1, then the value of x after 2nd iteration is ________.
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- 0.3043
- 0.2043
- 1.2043
- 1.3043
Correct Option: A
By Newton-Raphson Method,
| 1st iteration, x1 = x0 – | f'(0) |
| = 1 - | = 1 - | = | f'(1) | 10 | 2 |
Where f(x) = x3 + 2x2 + 3x – 1 ⇒ f(1) = 5
f'(x) = 3x2 + 4x + 3 ⇒ f'(1) = 10
| 2nd iteration, x2 = x1 | = 0.5 - | = 0.3043 | f'(x1) | f'(0.5) |
