Computer Oriented Numerical Methods (BCA) 3rd Sem Previous Year Solved Question Paper 2022

The Regula-Falsi method (also known as the False Position method) is a numerical technique for finding the roots of an equation by iteratively narrowing down the interval where the root lies. To solve the equation 3−5+3=0x3−5x+3=0, we can apply this method. Here are the steps:

1. Select an interval [a,b] such that f(a) and f(b) have opposite signs, which ensures there is a root within the interval.

2. Calculate the next approximation c using the formula: c=f(b)−f(a)a⋅f(b)−b⋅f(a)​

3. Calculate f(c).

4. If ∣∣f(c)∣ is smaller than a predefined tolerance (a small positive value), consider c as the root, or if the number of iterations exceeds a maximum limit, stop.

5. If f(c) and f(a) have opposite signs, update b=c; otherwise, update a=c.

6. Repeat steps 2-5 until you find a satisfactory approximation for the root.

Let's start with an initial interval [][a,b], and I'll perform the first iteration:

Initial interval: []=[1,2][a,b]=[1,2]

=(1)=1−5+3=−1f(a)=f(1)=1−5+3=−1

=(2)=8−10+3=1f(b)=f(2)=8−10+3=1

So, we have opposite signs at a and b, which is good. Now, we calculate c:

=1⋅1−2⋅(−1)1−(−1)=32=1.5c=1−(−1)1⋅1−2⋅(−1)​=23​=1.5

Now, we calculate f(c):

(1.5)=(1.5)3−5(1.5)+3f(1.5)=(1.5)3−5(1.5)+3

You can continue the iterations, updating the interval [a,b] and calculating f(c) until ∣∣f(c)∣ is smaller than your chosen tolerance or until reach a predefined maximum number of iterations.

The Regula-Falsi method iteratively refines the approximation for the root. Be sure to apply the method for subsequent iterations to narrow down the root further.