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Manipal MET2020MathematicsApplication of Derivatives

By Newton-Raphson method, the positive root of the equation x^4-x-10=0 is

Options

  1. A1.871
  2. B1.868
  3. C1.856
  4. DNone of these

Correct answer

A. 1.871

Step-by-step solution

Given, f(x)=x^4-x-10 We assume x₀=2 is the approximate root of f(x) . Then, h=- f (x₀ ) f (x₀ ) =- f(2) f(2) array ll & h=- [ (2)^4-2-10 4(2)^3-1 ] & h=- [ 16-12 31 ]= -4 31 & h=-0.129 array Positive square root of f(x) by Newton-Raphson method, aligned x₁=x₀+h & =2+(-0.129) & =2-0.129=1.871 aligned

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