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x^4 + 4bx^3 + (a^2 + 4b^2 + l^2)x^2 + 2(b(a^2+l^2)-m*l^2)x + a^2l^2 = 0

For some specific values of the unknown coefficients we can get the root. But how could we get the roots of the equation for unknown values of the coefficients ,i.e., how could we get the roots for any values of the coefficients ?

Aditya Das
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  • [quartics have a closed form solution](https://en.m.wikipedia.org/wiki/Quartic_equation) – Him Aug 19 '23 at 07:05

1 Answers1

0

This is the answer...

import sympy as sp

# symbolic variables
x, a, b, l, m = sp.symbols('x a b l m')

# equation
polynomial = x**4 + 4*b*x**3 + (a**2 + 4*b**2 + l**2)*x**2 + 2*(b*(a**2+l**2)-m*l**2)*x + a**2*l**2

# Find the roots of the polynomial equation
roots = sp.solve(polynomial, x)

for root in roots:
    print(root)
D.L
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Suriyaprakash G
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  • Your answer could be improved with additional supporting information. Please [edit] to add further details, such as citations or documentation, so that others can confirm that your answer is correct. You can find more information on how to write good answers [in the help center](/help/how-to-answer). – Diego Borba Aug 21 '23 at 12:28