GATE2018 CE-2: 20

Question

The quadratic equation $2x^2 - 3x +3=0$ is to be solved numerically starting with an initial guess as $x_0=2$. The new estimate of $x$ after the first iteration using Newton-Raphson method is _________

Answer 1

F(x) = 2x^2 - 3x + 3 , x0 = 2

using Newton Raphson method

X(n+1) = Xn - F(Xn)/F’(Xn)

So, F(x) = 2x^2 - 3x + 3

& F’(x) = 4x - 3

F(2) = 5

F’(2) = 5

therefore X1 = X0 - F(X0)/ F’(X0)

= 2-1 = 1