quadratic

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quadratic.roots(a, b, c, verbose=False)

Return the two roots in the quadratic equation:

a*x**2 + b*x + c = 0

or written with math typesetting

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

The returned roots are real or complex numbers, depending on the values of the arguments a, b, and c.

Parameters :

a: int, real, complex :

coefficient of the quadratic term

b: int, real, complex :

coefficient of the linear term

c: int, real, complex :

coefficient of the constant term

verbose: bool, optional :

prints the quantity b**2 - 4*a*c and if the roots are real or complex

Returns :

root1, root2: real, complex :

the roots of the quadratic polynomial.

Raises :

ValueError: :

when a is zero

See also

Quadratic

which is a class for quadratic polynomials that also has a Quadratic.roots() method for computing the roots of a quadratic polynomial. There is also a class linear.Linear in the module linear (i.e., linear.Linear).

Notes

The algorithm is a straightforward implementation of a very well known formula [R1].

References

[R1]	(1, 2) Any textbook on mathematics or Wikipedia.

Examples

>>> roots(-1, 2, 10)
(-5.3166247903553998, 1.3166247903553998)
>>> roots(-1, 2, -10)
((-2-3j), (-2+3j))

Alternatively, we can in a doc string list the arguments and return values in a table

Parameter	Type	Description
a	float/complex	coefficient for quadratic term
b	float/complex	coefficient for linear term
c	float/complex	coefficient for constant term
r1, r2	float/complex	return: the two roots of the quadratic polynomial

class quadratic.Quadratic(a, b, c)

Representation of a quadratic polynomial:

\[ax^2 + bx + c\]

Example:

>>> q = Quadratic(a=2, b=4, c=-16)
>>> print q
2*x**2 + 4*x - 16
>>> r1, r2 = q.roots()
>>> r1
2.0
>>> r2
-4.0
>>> q(r1), q(r2)  # check
(0.0, 0.0)
>>> repr(q)
'Quadratic(a=2, b=4, c=-16)'

Methods

__call__(x)
roots()	Return the two roots of the quadratic polynomial.
value(x)	Return the value of the quadratic polynomial for x.

__call__(x)

__init__(a, b, c)

The arguments a, b, and c are coefficients in the quadratic polynomial:

a*x**2 + b*x + c

or

\[ax^2 + bx + c\]

Argument	Type	Description
a	float/complex	coefficient for quadratic term
b	float/complex	coefficient for linear term
c	float/complex	coefficient for constant term

Raises :

ValueError: :

When a is too close to zero.

__module__ = 'quadratic'

__repr__()

__str__()

roots()

Return the two roots of the quadratic polynomial. The roots are real or complex, depending on the coefficients in the polynomial.

Let us define a quadratic polynomial:

>>> q = Quadratic(a=2, b=4, c=-16)
>>> print q
2*x**2 + 4*x - 16

The roots are then found by

>>> r1, r2 = q.roots()
>>> r1
2.0
>>> r2
-4.0

value(x)

Return the value of the quadratic polynomial for x.

Example:

>>> q = Quadratic(a=2, b=4, c=-16)
>>> print q
2*x**2 + 4*x - 16
>>> q(1)
-10
>>> q(-2.5)
-13.5

class quadratic.Cubic(a, b, c, d)

Bases: quadratic.Quadratic

Evaluation of a cubic polynomial \(ax^3 + bx^2 + cx + d\).

Methods

__call__(x)
roots()
value(x)

__call__(x)

__init__(a, b, c, d)

__module__ = 'quadratic'

__repr__()

__str__()

roots()

value(x)