GATE Civil Engineering (CE) 2018 Shift 2 Solved Paper

Question : 26 of 65

Marks: +1, -0

The quadratic equation

2 x^{2}-3 x+3=0

is to be solved numerically starting with an initial guess

x_{0}=2

. The new estimate of

x

after the first iteration using Newton-Raphson method is

Solution:

Given

f(x)=2 x^{2}-3 x+3, x_{0}=2

f^{'}(x)=4 x-3

By Newton-Rapshon

x_{1} \;\; =x_{0}-\;{f(x_{0})}/{f^{'}(x_{0})}=2-\;{2(2)^{2}-3(2)+3}/{4(2)-3}

\;\; =2-\;{5}/{5}=1

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