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Engineering Mathematics
Numerical Methods
GATE 2010
Easy

A root of the equation x⁴−3x+1=0 needs to be found using the Newton-Raphson method. If the initial guess, x0, is taken as 0, then the new estimate, x1, after the first iteration is

  • 1/3
  • B−1/3
  • C3
  • D−3

Explanation

f(x)=x⁴−3x+1, f'(x)=4x³−3. At x0=0: f(0)=1, f'(0)=−3. x1=x0−f(x0)/f'(x0)=0−1/(−3)=1/3.

Source: GATE CH 2010 (2010)

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