Quadratic Formula#

pyquations.algebra.quadratic_formula.quadratic_formula(a: float, b: float, c: float) → Tuple[complex, complex][source]

Calculates the roots of a quadratic equation.

The quadratic formula is a closed-form expression describing the solutions of a quadratic equation. Other ways of solving quadratic equations, such as completing the square, yield the same solutions. [1]

\[ax^2 + bx + c = 0\]
Parameters:

  • a (float) – Coefficient of the quadratic term (x^2). Must not be zero.

  • b (float) – Coefficient of the linear term (x).

  • c (float) – Constant term.

Returns:

A tuple containing two roots of the quadratic

equation. The roots may be real or complex numbers depending on the discriminant.

Return type:

Tuple[complex, complex]

Raises:

ValueError – If ‘a’ is zero, as this would not represent a quadratic equation.

Examples

>>> quadratic_formula(1, -3, 2)
(2.0, 1.0)

>>> quadratic_formula(1, 2, 5)
(-1+2j, -1-2j)
Resources:

References