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curriculum/challenges/english/blocks/learn-interfaces-by-building-an-equation-solver/6650583d9d9a194714da47f0.md

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--description--

The roots of quadratic equations can be found by applying the formula:

\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} = \frac{-b \pm \sqrt{\Delta}}{2a} \]

After the if statement, create two variables: assign them the root obtained by taking the plus sign between \( b \) and the square root of the discriminant in the formula above, and the root obtained by taking the minus sign. Then, return a list containing your two new variables.

--hints--

Your solve method should return a list containing the correct solutions.

js
({ test: () => runPython(`
eq = QuadraticEquation(-1, 2, 3)
assert eq.solve() == [-1, 3] or eq.solve() == [3, -1]
`) })

--seed--

--seed-contents--

py
from abc import ABC, abstractmethod
import re


class Equation(ABC):
    degree: int
  
    def __init__(self, *args):
        if (self.degree + 1) != len(args):
            raise TypeError(
                f"'Equation' object takes {self.degree + 1} positional arguments but {len(args)} were given"
            )
        if any(not isinstance(arg, (int, float)) for arg in args):
            raise TypeError("Coefficients must be of type 'int' or 'float'")
        if args[0] == 0:
            raise ValueError("Highest degree coefficient must be different from zero")
        self.coefficients = {(len(args) - n - 1): arg for n, arg in enumerate(args)}

    def __init_subclass__(cls):
        if not hasattr(cls, "degree"):
            raise AttributeError(
                f"Cannot create '{cls.__name__}' class: missing required attribute 'degree'"
            )

    def __str__(self):
        terms = []
        for n, coefficient in self.coefficients.items():
            if not coefficient:
                continue
            if n == 0:
                terms.append(f'{coefficient:+}')
            elif n == 1:
                terms.append(f'{coefficient:+}x')
            else:
                terms.append(f"{coefficient:+}x**{n}")
        equation_string = ' '.join(terms) + ' = 0'
        return re.sub(r"(?<!\d)1(?=x)", "", equation_string.strip("+"))        

    @abstractmethod
    def solve(self):
        pass
        
    @abstractmethod
    def analyze(self):
        pass
        
class LinearEquation(Equation):
    degree = 1
    
    def solve(self):
        a, b = self.coefficients.values()
        x = -b / a
        return x

    def analyze(self):
        slope, intercept = self.coefficients.values()
        return {'slope': slope, 'intercept': intercept}

class QuadraticEquation(Equation):
    degree = 2

    def __init__(self, *args):
        super().__init__(*args)
        a, b, c = self.coefficients.values()
        self.delta = b**2 - 4 * a * c
--fcc-editable-region--
    def solve(self):
        if self.delta < 0:
            return []
--fcc-editable-region--
    def analyze(self):
        pass


lin_eq = LinearEquation(2, 3)
print(lin_eq)
quadr_eq = QuadraticEquation(11, -1, 1)
print(quadr_eq)