In the Testequationsstart. java $$ file $($which you will save as Testequations. java$),$ you are given an

abstract class for equations in one variable: Equation. It represents an equation by the coefficient$($s$)$ of a variable

$x$ and its powers, and has an abstract findsolution method that returns an array of double giving the root$($s$)$ of

the equation. You will write two concrete classes that extend this abstract class, as shown in the following UML

diagram:

The first class, LinearEquation, represents a linear equation of the form $ax+b=0.($Thus$,$ the coefficients array

will have two entries.$)$ It has two constructors:

public LincarEquation$($double$[]$ coefficients$)$

public LinearEquation$($double a$,$ double b$)//$ used to populate the cocficients property

Implement the

method, which will return an array of one double with the solution. Also,

implement a tastring$()$ method that returns a string in the form $ax+b-$ where both the numbers are

displayed with two digits to the right of the decimal point.

The second class, puadraticfquation, represents a quadratic equation of the form $a{x}^2+bx+c=0.($Thus$,$ the

array will have three entries.$)$ It has two constructors:

public Quadratickquation$($double$[]$ cocfficients$)$

public quadraticequation$($double a$,$ double b$,$ double c$)///$ used to populate the coefficients property

Implement the findsolution$()$ method, which will return:

if there are no solutions to the equation.

an array of length one giving the root of the equation if there is only one root

an array of length two giving the roots of the equation if there are two roots

Hint: Put the coefficients for the quadratic equation into variables named $a,b,$ and $c$ to make the code easier to

read.

Also, implement a method that returns a string in the form $(a{x}^2+bx+c-a)$ where all the numbers

are displayed with two digits to the right of the decimal point. Use $($uatebz to produce a superscript $2$ in the

output.

Use the Testequationsstart. java darr file as your starting point, and save it as Testequations $.$ java

Here is what the output of your finished program should look like:

When You Finish

Upload the TestEquation. java file. Remember to put comments at the start of the file that give your name, the

date you wrote the code, and a description of the program. The description must be sufficient for someone who

has not read the assignment to understand what kind of input is expected, what processing occurs, and what the

output is$.$