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Quantitative Finance

Numerical Methods

Concept Quizzes

Root Approximation - Bisection
Newton Raphson Method

Newton Raphson Method

Let $f(x) = x^3 - 72x - 220.$ Given that $f(x)=0$ has a root near $x = 12,$ compute $x_1$ by using Newton-Raphson method starting with $x_0=12.$

\frac{379}{45}

\frac{919}{90}

\frac{919}{72}

\frac{1241}{90}

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by Brilliant Staff

By using the Newton-Raphson method, find the positive root of the following quadratic equation correct to $5$ significant figures: $x^2 + 9x - 5 = 0.$

Start with $x_0 = 2.2.$

1.04986

0.52493

0.73432

2.23607

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by Brilliant Staff

Use the Newton-Raphson method, correct to $5$ significant figures, to get the root near $x = 2$ of the equation $f(x) = x^3 - 3x - 8.$

2.84803

2.49203

3.20404

2.13603

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by Brilliant Staff

The equation $f(x) = 4e^x - 12$ has a root near $x = 1.$ Use the Newton-Raphson method to calculate the root correct to $5$ significant figures.

1.23594

0.82396

0.96128

1.09861

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by Brilliant Staff

Let $f(x) = 4 x^2 - 8.$ Which of the following is the correct representation of $x_{n+1}$ that Newton-Raphson method leads to?

\left( x_n + \frac{1}{2 x_n} \right)

\frac{1}{2} \left( 4 x_n + \frac{2}{ x_n} \right)

2 \left( 4 x_n - \frac{2}{x_n} \right)

\frac{1}{2} \left( x_n + \frac{2}{x_n} \right)

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by Brilliant Staff

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