Write a program that prompts the user to input the three coefficients a, b, and c of a quadratic equation; i.e., an equation of the form ax2 + bx + c = 0. The program should display the solutions of this equation (also known as zeros, or roots of the function f(x) = ax2 + bx + c) in the following manner: 1. If the equation has one solution, display ONE SOLUTION: followed by the solution, displayed with 4 digits printed out after the decimal place, as shown in the examples below. 2. If the equation has two real solutions, display TWO REAL SOLUTIONS: followed by the two solutions, each displayed with 4 digits printed out after the decimal place, as shown in the examples below. The smaller of the two should be displayed first. 3. If the equation has solutions that are not real numbers, display COMPLEX SOLUTIONS: followed by two solutions displayed in the form + i, where each and should be displayed with 4 digits printed out after the decimal place, as shown in the examples below. The solution with the minus i term should be displayed first in your output (so, for example, 1.0000 - 2.5000i should be displayed before 1.0000 + 2.5000i). Also, your displayed solution should NOT have a negative sign in front of a 0.0000; for example, COMPLEX SOLUTIONS: x = -0.0000 - 1.9634i and x = -0.0000 + 1.9634i should be displayed instead as COMPLEX SOLUTIONS: x = 0.0000 - 1.9634i and x = 0.0000 + 1.9634i Dont bother trying to omit the zeros. Also, take care not to display outputs such as COMPLEX SOLUTIONS: x = 0.1493 - -1.0112i and x = 0.1493 + -1.0112i with the - - and + - before the imaginary term. Instead, it should be displayed as COMPLEX SOLUTIONS: x = 0.1493 - 1.0112i and x = 0.1493 + 1.0112i 4. If 0 is entered as input for a, do no calculations and output the message The equation is not quadratic For example, a run might look like this: Enter x^2 coefficient: 0 Enter x^1 coefficient: -2 Enter x^0 coefficient: 1 The equation is not quadratic OR Enter x^2 coefficient: 1 Enter x^1 coefficient: -2 Enter x^0 coefficient: 1 ONE SOLUTION: x = 1.0000 OR Enter x^2 coefficient: 3 Enter x^1 coefficient: 5 Enter x^0 coefficient: 1 TWO REAL SOLUTIONS: x = -1.4343 and x = -0.2324 OR Enter x^2 coefficient: -1 Enter x^1 coefficient: 2 Enter x^0 coefficient: 7 TWO REAL SOLUTIONS: x = -1.8284 and x = 3.8284 OR Enter x^2 coefficient: 2.1 Enter x^1 coefficient: 4 Enter x^0 coefficient: 10 COMPLEX SOLUTIONS: x = -0.9524 - 1.9634i and x = -0.9524 + 1.9634i In the last case, note that the letter that is printed out to represent the square root of 1 is the letter i, not the letter j! Python has some functions that produce complex values, but when you print these values, they display the letter j to represent 1. I dont want that instead, your program should calculate the imaginary coefficient and include code that prints out the string "i". Do NOT use the cmath module, the complex function, the .imag attribute or any Python functions that perform replacements in strings. (If you dont know what any of those are, dont worry about it.) Note: This problem has six visible test cases on Gradescope. You will see if your code passes these six test cases. In addition, it has three invisible test cases, which you will not be able to see until after grades are released (you will not see if your code passed or did not pass these). So make sure you run additional tests on your own to cover all the possible inputs described! (You must work out the correct output in your test cases.) Specifications: your program must ask for and accept coefficients from the user. Use the input prompt format as specified in the sample runs above. display the type of solutions as above. If there is exactly one solution, it is acceptable if the program occasionally misidentifies it (due to float weirdness, as discussed in class). However, it should work with the example test cases. display all solutions with precisely four digits printed after each decimal (for complex solutions, four digits after the decimal for both real and imaginary parts). use the letter i to represent 1 in output, not the letter j. NOT use the cmath module, the complex function, the .imag attribute, or any Python functions that perform replacements in strings. Remember that to pass the test cases on Gradescope, formatting, including spacing, must match exactly as in the sample runs above.