Question

A quadratic equation x2-4x+4=0 is defined with an initial guess of 3 and 2.5. Find the approximated value of root using Secant Method.

Answer 1

Answer:

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Answer 2

Answer:

Approximate value of root is 2.333

Step-by-step explanation:

Here,

Given :

X0 = 3

X1 = 2.5

f(x) = $x^2 - 4x + 4 = 0$

To find : Approximate value of root of the given equation

Formula :  $X2 = \frac{X0 - X1}{f(X0) - f(Xi)} * f(X1)$

Solution :

Here, we know that,

X0 = 3, X1 = 2.5

Therefore, f(Xo) = 1, f(X1) = 0.25

(By inserting value of X0 and X1 in the given equation)

Now,

By Secants formula,

$X2 = X1 - \frac{X0 - X1}{f(X0) - f(X1)} * f(X1)$

$X2 = 2.5 - \frac{3 - 2.5}{1 - 0.25} * 0.25$

Therefore, by solving above equation,

We get,

X2 = 2.33

Therefore, approximate value of root of equation is 2.33

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