Quadratic equations
===================

Write and save the following functions into the same file named
``quadratic.py``.

#. :py:func:`real_roots` that takes three parameters ``a``, ``b`` and
   ``c``, corresponding to the coefficients of a quadratic equation
   :math:`y=ax^2+bx+c` with two different real roots, and returns its
   roots.

   See the following examples:
   
   .. literalinclude:: quadratic1.txt
      :language: python3
      :lines: 5-8

   .. note::
      More tests are provided in the :download:`quadratic1.txt<quadratic1.txt>` file.

#. :py:func:`has_real_roots` that takes three parameters ``a``, ``b``
   and ``c``, corresponding to the coefficients of a quadratic
   equation :math:`y=ax^2+bx+c`, and retuns ``True`` if the quadratic
   equation has real roots and ``False`` otherwise.

   See the following examples:
   
   .. literalinclude:: quadratic2.txt
      :language: python3
      :lines: 5-8

   .. note::
      More tests are provided in the :download:`quadratic2.txt<quadratic2.txt>` file.
         
#. :py:func:`is_a_root` that takes five parameters ``a``, ``b``, ``c``
   corresponding to the coefficients of a quadratic equation
   :math:`y=ax^2+bx+c`, ``x`` corresponding to a candidate root ``x``,
   and ``eps`` corresponding to a tolerance. This function returns
   ``True`` if ``x`` is a root of the quadratic equation taking into
   account the given tolerance, i. e., when ``abs(y) <= eps``, and
   ``False`` otherwise.

   See the following examples:
   
   .. literalinclude:: quadratic3.txt
      :language: python3
      :lines: 12-25

   .. note::
      More tests are provided in the :download:`quadratic3.txt<quadratic3.txt>` file.

.. rubric:: Solutions

A solution of these functions is provided in the
:download:`quadratic.py<solutions/quadratic.py>` file.