(Algebra: quadratic equations) Design a class named QuadraticEquation for a quadratic equation $a x^2+b x+c-0$. The class contains:

- Private data fields $a, b$, and c that represent three coefficients.
- A constructor with the arguments for $a, b$, and $c$.
- Three getter methods for a, b, and c.
- A method named getDiscriminant () that returns the discriminant, which is $b^2-4 a c$.
- The methods named getRoot1 ( ) and getRoot2 () for returning two roots of the equation

$r_1=\frac{-b+\sqrt{b^2-4 a c}}{2 a} \text { and } \quad r_2=\frac{-b-\sqrt{b^2-4 a c}}{2 a}$

These methods are useful only if the discriminant is nonnegative. Let these methods return 0 if the discriminant is negative.

Draw the UML diagram for the class then implement the class. Write a test program that prompts the user to enter values for $a, b$, and $c$ and displays the result based on the discriminant. If the discriminant is positive, display the two roots. If the discriminant is 0 , display the one root. Otherwise, display "The equation has no roots." See Programming Exercise $3.1$ for sample runs.

Solution

VerifiedTo start, we're going to make a UML diagram of the class: