Thank you for visiting Write a computer program using any language of your choice to implement Bairstow s method for finding the roots of a given polynomial function Program. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!
Answer :
This program takes the degree and coefficients of a polynomial function as input. It implements Bairstow's method to find the roots of the polynomial and prints the intermediate tables for each quadratic factor. Finally, it prints the linear and constant factors.
Here's an example program written in Python that implements Bairstow's method for finding the roots of a polynomial function:
```python
def bairstow(degree, coefficients):
n = degree
b = [0] * (n + 1)
c = [0] * (n + 1)
# Initialize the coefficients of b and c
for i in range(n + 1):
b[i] = coefficients[i]
c[0] = b[0]
# Bairstow's method iterations
while n > 2:
u = v = du = dv = 0
e = 1.0
while e > 0.0001:
b[n - 1] += du
b[n] += dv
for i in range(n - 1, 1, -1):
b[i - 1] += u * b[i] + du
c[i] = b[i] + u * c[i + 1] + v * c[i + 2] + dv
b[0] += u * b[1] + du
c[1] = b[1] + u * c[2] + v * c[3] + dv
det = c[2] * c[2] - c[1] * c[3]
du = (-b[0] * c[2] + b[1] * c[1]) / det
dv = (-b[1] * c[2] + b[0] * c[3]) / det
u += du
v += dv
e = abs(du) + abs(dv)
print(f"\nITERATION: Degree {n}")
print(f"b: {b[:n+1]}")
print(f"c: {c[:n+1]}")
# Print the quadratic factor
print("Quadratic Factor:")
print(f"x² + {u:.4f}x + {v:.4f}")
n -= 2
# Print the linear and constant factors
if n == 2:
print("\nLinear Factor:")
print(f"x + {b[1]:.4f}")
if n == 1:
print("\nConstant Factor:")
print(f"{b[0]:.4f}")
# Test cases
polynomials = [
[1, 2, 0, 3, 4],
[6, 8, 5, -32, -1, 40, 0, 0, 25],
[8, 739, 37, 446, -180, -1928, -256, 1920],
[7, -11, 41, -183, 231, 21, -265, 150]
]
for i, polynomial in enumerate(polynomials):
degree = len(polynomial) - 1
print(f"\nTest case {i+1}:")
print("Polynomial coefficients:", polynomial)
bairstow(degree, polynomial)
```
This program takes the degree and coefficients of a polynomial function as input. It implements Bairstow's method to find the roots of the polynomial and prints the intermediate tables for each quadratic factor. Finally, it prints the linear and constant factors.
You can run this program with the provided test cases or modify it to input your own polynomial coefficients.
Learn more about polynomial here
https://brainly.com/question/30703661
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Rewritten by : Jeany
