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GATE 2018 CE (CE2) – Question 30

Engineering Mathematics · Numerical Methods: Error analysis, algebraic equations, interpolation, differentiation, integration, ODEs · 1 mark · Numerical answer

Solve $2x^2-3x+3=0$ numerically starting at $x_0=2$. The first Newton–Raphson estimate is ______.

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Correct answer: 1 to 1

Explanation

Let $f(x)=2x^2-3x+3$, so $f^\prime(x)=4x-3$. At $x_0=2$, both f and its derivative equal 5. Newton’s update is $x_1=2-5/5=1$. This is only the first iterate; the quadratic has no real root.