Newton – Raphson method is used to compute a root of the equation x² + 4x − 9 = 0 with 1 as the initial value. The approximate value after one iteration is…
Newton – Raphson method is used to compute a root of the equation x² + 4x − 9 = 0 with 1 as the initial value. The approximate value after one iteration is ________.
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Correct answer: (A) 1.571
Explanation
The keyed 1.571 comes from x³ + 4x − 9 = 0 (the cube seems lost in the source): f(1) = −4, f'(1) = 3 + 4 = 7, so x₁ = 1 + 4/7 ≈ 1.571. With x² instead, x₁ would be 1.667.