Use RegulaFalsi Method to find a real root of the equation xe^x - 2 = 0 correct to two decimal places within the interval [1,0]?

Question

Kindly Answer me Quick Please...!!!

& Sir Kindly Step by Step

Answer 1

The formula for regula falsi is as follow:

 

Suppose the root is located between x = a and x = b with a < b

 

then x₁ = a -[(b-a) f(a)]/[f(b) - f(a)]

 

Let us suppose that f(a) < 0 and f(b) > 0.

 

f(x₁) will be either greater or less than zero (unless you got the root exactly!)

 

if f(x₁) < 0, replace a with x₁ and f(a) with f(x₁) in the formula and repeat the process to get x₂

 

if f(x₁) > 0, replace b with x₁ and f(b) with f(x₁) in the formula and repeat the process to get x₂

 

I will do the first round for you, then you follow until the 2nd decimal does not change

 

For your problem a = 0 and b = 1

f(0) = -2 and f(1) = .718282

 

x₁ = 0 - [1-0](-2)/[.718282-(-2)] = .735759

 

f(x₁) < 0 so replace a with x₁ and repeat.  You go from here!