Problem $1.$ Quadratic Equations python

A quadratic equation has the form:

a x $2+$ b x$+$ c$=0$

The two solutions $($called roots$)$ are given by the formula:

x $1,2=$b$\backslash$pm $$ b $24$ a c

$2$ a $(1)$

Write a program with a loop that :

a$)$ solves quadratic equations with coefficients read from the terminal,

b$)$ visualizes the corresponding quadratic function y$=$ ax

$2+$bx $+$c using the matplotlib.pyplot module

$($replacing module pylab used in the book$).$

Details:

$1.$ The program consists of a main while loop $($an infinite loop$)$ in which the user is prompted to enter

values for coefficients a$,$ b$,$ and c$.$ Assume the user types valid float numbers from the terminal. The

program converts the input to float type and then uses formula $(1)$ above to compute solutions x$1$ and

x$2,$ as follows:

$$ if b $24$ ac $<0$ then the solutions are complex numbers $($i$.$e$.$ not real$)$ and the program displays

the string $$no real solutions$,$

$$ if b$24$ ac $=0$ then x$1=$x$2$ and the program displays: $$one solution: $$ followed by the value x$1.$

$$ if b $24$ ac $>0$ then the solutions are distinct and the program displays $$two solutions: $$

followed by the values of x$1$ and x$2.$

To keep the problem simple we can assume that the user never enters a value for coefficient a that is

equal to $0.$

To stop the loop and end the program the user just types the ENTER key instead of the string for

coefficient a$.$

$2.$ Within the main loop, after printing the values of the real solutions $($if any$)$ to the terminal the

program displays the graphic of the quadratic function y$=$ ax

$2+$bx $+$c using the matplotlib.pyplot

module. The chart should use $150$ points.

$$ If the function has real roots $($one or two$)$ make sure the roots are visible on the chart. E$.$g$.$ if the

roots are $-1$ and $3$ use a domain interval for values x $($on the $0$x axis$)$ that includes $-1$ and $3,$ like

$[-3,5].$

$$ If the function has no real roots, then center the function domain $($x values$)$ on the function$$s

minimum or maximum value, which is x opt $=$b

$2$ a $.$

$$ Pick your own approach to select the function$$s domain while complying with the above

requirements.

$3.$ Insert the source code from p$1\_...$py into the h$1.$doc Word document. The grader appreciates if you

use syntax highlighting, although it is not required.

$4.$ Take a screenshot of the PC desktop showing the Spyder Python shell and the matplotlib figure

window and paste it in the h$1.$doc file after the source code.

The screenshot may look similar to this one:

Here is a sample user session on the terminal:

Problem $2.$ Pythagorean Numbers

The lengths $($a$,$b$,$c$)$ of the three sides of a right triangle are related by this well$-$known formula:

a$2+$ b$2=$ c$2.$

A Pythagorean triple consists of three positive integer numbers bound by the above relation. An

example of a triple is $(3,4,5).$

Enter a: $1$

Enter b: $2$

Enter c: $1$

one solution: $-1\mathrm{.}00000$

Enter a: $3$

Enter b: $0$

Enter c: $1$

no real solutions

Enter a: $1$

Enter b: $-1$

Enter c: $-6$

two solutions: x$1=-2\mathrm{.}00000$ x$2=3\mathrm{.}00000$

$($user types CTRL$-$Z on Windows to enter EOF and finish the program