In the Newton-Raphson method, an initial guess of \(x_0 = 2\) is made and the…

GATE · 2014 · CS · Set 2 · Computer Science & IT

In the Newton-Raphson method, an initial guess of x0=2x_0 = 2 is made and the sequence x0,x1,x2x_0,x_1,x_2 … is obtained for the function

0.75x3−2x2−2x+4=00.75x^3 - 2x^2 - 2x + 4 = 0

Consider the statements

(I) x3=0x_3 = 0.

(II) The method converges to a solution in a finite number of iterations.

Which of the following is TRUE?

  1. A.

    Only I

  2. B.

    Only II

  3. C.

    Both I and II

  4. D.

    Neither I nor II

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