Find a root of the Equation, x2 − 4x −10 = 0 using bisection method.

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05-04-2022
Mathematics

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Find a root of the Equation, x2 − 4x −10 = 0 using bisection method.

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Akposevictoridn Akposevictoridn · Answer 1 · 2022-04-07T08:07:48-04:00

Using the bisection method, a root of the equation, is: x = -1.74 or x = 5.74.

What is the Bisection Method?

The bisection method is a method employed to approximately find the roots of an equation through repeated dividison of an interval until a relatively small interval is arrived at.

Given the equation:

x² - 4x - 10 = 0.

Applying the bisection method, we would have the following:

x² - 4x + (2²) - (2²) - 10 = 0

(x - 2)² - 14 = 0

Add 14 to both sides

(x - 2)² = 14

Take the square root of both sides

x - 2 = ±√14

x = 2 ± √14

x = 2 - √14 = -1.74

or x = 2 + √14 = 5.74

Therefore, using the bisection method, a root of the equation, is: x = -1.74 or x = 5.74.

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What is the Bisection Method?

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