The Homework $1$ topic is the creation of a $C$ language program to calculate and present the two

solutions of the following quadratic equation:

$a{x}^2+bx+c=0,$ where the coefficients $a,b,c$ are real numbers with $a0$

It is a fact that the solutions are either $2$ real numbers or $2$ complex conjugate numbers,

depending on the value of the discriminant, $D=b^2-4ac.$

Specifically,

If the discriminant satisfies $D0,$ then the $2$ quadratic roots are real numbers, given

by$,$

$x_{r_1}=\frac{-b+\sqrt[\phantom{2}]{D}}{2a}$

$x_{r_2}=\frac{-b-\sqrt[\phantom{2}]{D}}{2a}$

else, the $2$ roots are complex conjugate numbers, given by$,$

$x_{c_1}=$ Real $+j$ Imag $=(\frac{-b}{2a})+j(\frac{\sqrt[\phantom{2}]{-D}}{2a})$

$x_{c_2}=$ Real $-j$ Imag $=(\frac{-b}{2a})-j(\frac{\sqrt[\phantom{2}]{-D}}{2a})$

A C language code is provided but it's incomplete. There are gaps to be completed in order to

run correctly and to provide the correct answers. The Homework assignment consists of $4$ tasks

as detailed below:

Task $1(10$ points$)$: Provide the pseudocode that is relevant to this programming task

$($refer to Fig. $1).$

Task $2(10$ points$)$: Complete the flowchart that is relevant to this programming task

$($refer to Fig. $1).$

Task $3(10$ points$)$: Complete the gaps in the provided $C$ code using the correct syntax

and debug your code so that it runs correctly.

Task $4(10$ points$)$: Test your code using the provided test cases.$|$

$============================$

#include $$stdio$.$h$>$

#include $$math$.$h$>$

$/*$ This program finds the solutions of the quadratic equation $a{x}^2+b*x+c=0*/$

int main$()$

$\{$

$/*$ Define and initialize the variables$*/$

float D$,$ real$\_$root$1,$ real$\_$root$2,$ real$\_$part, imag$\_$part;

$/*$ Input the coefficients of the equation and ensure that a is not equal to zero$*/$

while $()\{$

printf$("$Specify the coefficients of the quadratic a $\{$:$x^2+bx+c,$

$")$;

printf$("$The value of the a coefficient must be non$-$zero"$)$;

$\}$

$/*$ Calculate the discriminant value$*/$

D $=$

$/*$ Write an if$/$else statement to check if the roots are real or complex numbers$*/$

if $()$

$\{$

real$\_$root$1=\frac{-b+sqrt(D)}{2*a}$;

real$\_$root$2=$

printf$("$The real roots of the $",)$;

printf$("",)$;

$\}$

else

$\{$

real$\_$part $=$

imag$\_$part $=$sqrt$(-$D$)/(2*$a$)$;

printf$("$The complex roots of the quadratic$\%\mathrm{.}2f{x}^2+\%\mathrm{.}2fx+\%\mathrm{.}2f$ are

$",a,b,c$;

printf$("$x$1=\%\mathrm{.}4f+j\%\mathrm{.}4f,x2=\%\mathrm{.}4f-j\%\mathrm{.}4f",$ real$\_$part,imag$\_$part,real$\_$part,imag$\_$part$)$:

$\}$

return $0$ ;

$\}$

$=================$

$1)$ In line $15$ of the code, write an appropriate command to define the variables of the

coefficients $ab$ and c as float variables. $(1$ point$)$

$2)$In line $17,$ initialize the variable $t$ to be equal to zero. $(1$ point$)$

$3)$In line $20,$ specify the correct condition for the while loop. If the condition is satisfied then the loop continues to run. $(1$ point$)$

$4)$ In line $23,$ write a command to receive numerical values and assign them to the

coefficients $ab$ and point$)$

$5)$ In line $26,$ complete the numerical expression for the discriminant value $Q1$ point$)$

$6)$ In line $29,$ specify the condition of the if$/$else statement so that the first part of the if$/$else statement produces the real roots and the second part of the if$/$else statement produces the complex roots. $(1$ point$)$

$7)$ In line $32,$ write the numerical expression so that the code can calculate the second real root. $(1$ point$)$

$8)$ In lines $33,34,$ write appropriate printf commands to obtain the following output when the code runs correctly with input values $ab$ c $2-5$

$[$ The real roots $of$ the quadratic $1\mathrm{.}00x^2+-5\mathrm{.}00x+6\mathrm{.}00$ are

$x1=3\mathrm{.}0000,x2=2\mathrm{.}0000]$

$9)$ In line $38,$ write the correct numerical expression for the real part of the complex roots.

$(1$ point$)$

$============$

Output:

If you enter the values $ab$ c the should produce the following result,

$[$ The real roots $of$ the quadratic $1\mathrm{.}00x^2+-2\mathrm{.}00x+-8\mathrm{.}00$ are

$x1=4\mathrm{.}0000,x2=-2\mathrm{.}0000]$

If you enter the values $ab$c the code should produce the following result,

$]$

Submit your completed code.