python program, make a program that will solve for the root values of a given equation, through different methods.• Step by step solution is not necessary to be shown in the program.• Inputs from the user for the following method are the following:o N

python program, make a program that will solve for the root values of a given equation, through different methods.• Step by step solution is not necessary to be shown in the program.• Inputs from the user for the following method are the following:o N

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import sympy as sp def newton_raphson(equation, x0, precision): x = sp.Symbol('x') f = sp.sympify(equation) f_prime = f.diff(x) iterations = 0 while True: fx = f.subs(x, x0) fpx = f_prime.subs(x, x0) x1 = x0 - fx / fpx if abs(x1 - x0) < precision: break x0 = x1 iterations += 1 root_value = x1 return iterations, root_value def secant(equation, xa, xb, precision): x = sp.Symbol('x') f = sp.sympify(equation) iterations = 0 while True: fx_a = f.subs(x, xa) fx_b = f.subs(x, xb) x1 = xa - (fx_a * (xb - xa)) / (fx_b - fx_a) if abs(x1 - xa) < precision: break xa = xb xb = x1 iterations += 1 root_value = x1 return iterations, root_value # User inputs for Newton-Raphson method equation = input("Enter the equation: ") x0 = float(input("Enter the initial value (x0): ")) precision = float(input("Enter the precision: ")) # Solve using Newton-Raphson method newton_iterations, newton_root = newton_raphson(equation, x0, precision) # User inputs for Secant method equation = input("Enter the equation: ") xa = float(input("Enter the initial value (xa): ")) xb = float(input("Enter the initial value (xb): ")) precision = float(input("Enter the precision: ")) # Solve using Secant method secant_iterations, secant_root = secant(equation, xa, xb, precision) # Print the results print("\nNewton-Raphson Method:") print("Iterations:", newton_iterations) print("Root Value:", newton_root) print("\nSecant Method:") print("Iterations:", secant_iterations) print("Root Value:", secant_root)

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Contributed on Jun 21 2023

Iane Joshua Paguio

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python program, make a program that will solve for the root values of a given equation, through different methods. • Step by step solution is not necessary to be shown in the program. • Inputs from the user for the following method are the following:

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import math def equation(x): # Define your equation here return x**2 - 4 def bisection_method(xl, xr, precision): if equation(xl) * equation(xr) >= 0: print("Assumption invalid. Please provide different initial values.") return iterations = 0 while abs(xr - xl) >= precision: iterations += 1 x = (xl + xr) / 2 if equation(x) == 0: break elif equation(x) * equation(xl) < 0: xr = x else: xl = x print("Bisection Method:") print("Validity of assumptions: Assumption valid") print("Complete iterations:", iterations) print("Root value:", x) def false_position_method(xl, xr, precision): if equation(xl) * equation(xr) >= 0: print("Assumption invalid. Please provide different initial values.") return iterations = 0 while abs(xr - xl) >= precision: iterations += 1 x = (xl * equation(xr) - xr * equation(xl)) / (equation(xr) - equation(xl)) if equation(x) == 0: break elif equation(x) * equation(xl) < 0: xr = x else: xl = x print("False-Position Method:") print("Validity of assumptions: Assumption valid") print("Complete iterations:", iterations) print("Root value:", x) # Main program print("Root Solver Program") print("===================") # Get user inputs equation_string = input("Enter the equation (e.g., x**2 - 4): ") xl = float(input("Enter the initial value for XL: ")) xr = float(input("Enter the initial value for XR: ")) precision = float(input("Enter the precision: ")) # Convert the equation string to a function exec("def equation(x):\n return " + equation_string) # Solve using the Bisection method bisection_method(xl, xr, precision) print() # Solve using the False-Position method false_position_method(xl, xr, precision)

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Contributed on Jun 21 2023

Iane Joshua Paguio

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