Cubic Equation

Yaser Rahmati | یاسر رحمتی

In algebra, a cubic equation in one variable is an equation of the form:

$$ax^{3} + bx^{2} + cx + d = 0$$

in which $a$ is nonzero. The solutions of this equation are called roots of the cubic function.

Solving Equations

SymPy’s solve() function can be used to find solutions to equations. When you input an expression with a symbol representing a variable, such as $x$, solve() calculates the value of that symbol. This function always makes its calculation by assuming the expression you enter is equal to zero—that is, it prints the value that, when substituted for the symbol, makes the entire expression equal zero.

Example

Determine the roots of the cubic equation $2x^3+3x^2–11x–6=0$.

import sympy as sp

# Define the symbolic variable
x = sp.symbols('x')

# Define the function symbolically
expr = 2*x**3 +3*x**2 - 11*x -6

sp.solve(expr)

The point(s) where its graph crosses the x-axis, is a solution of the equation. The number of real solutions of the cubic equations is same as the number of times its graph crosses the x-axis.

sp.plot(expr , (x, -5, 3))

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