In what concerns the continuous evaluation solving exercises grade during the semester, you should submit until 23:59 of October 26th
(this exercise will still be available for submission after that deadline, but without couting towards your grade)
[to understand the context of this problem, you should read the class #03 exercise sheet]

[IP020] I am root

Quadratic equations play a fundamental role in algebra and mathematics. In this exercise, you will write a program that calculates the roots of a quadratic equation given its coefficients.

The Problem

Write a program that calculates the roots of a quadratic equation of the form: \[ ax^2 + bx + c = 0 \] Remember that the roots can be real or complex. Use math.sqrt in your calculations.

Input

The input consists of three floating-point numbers:

• The coefficient a
• The coefficient b
• The coefficient c

Output

The output should display the roots of the equation in the following formats:

• For one real root: "R = [value]"
• For two distinct real roots: R1 = [value]" and "R2 = [value]"
• For two complex roots: "R1 = [real_part] + [imaginary_part]i" and "R2 = [real_part] - [imaginary_part]i"

All the printed numbers should be rounded to two decimal places.

Constraints

The following limits are guaranteed in all the test cases that will be given to your program:

1
-5
6

R1 = 3.0
R2 = 2.0

1
4
5

R1 = -2.0 + 1.0i
R2 = -2.0 - 1.0i

1
-4
4

R = 2.0