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