$(30\%)$ Conditionals, Logical Operators, and Loops.

Problem $4\mathrm{.}1.(10\%)$ Consider the quadratic equation $a{x}^2+bx+c=0,$ where $a,b,$ and $c$ are given

constants. Using conditional statements, display the following text for the $3$ possible cases:

Case $1.$ "Real and distinct roots" when $b^2>4ac.$

Case $2.$ "Real and repeated roots" when $b^2=4ac.$

Case $3.$ "Complex roots" when

Case $4.$ "Invalid entry" when none of the previous conditions is met.

Additionally, display the solutions $($roots$)$ of the quadratic equation. Test your code with $3$ different sets of

values of $a,b,$ and $c$ of your choice, so that each of the three possible outcomes of your code are evaluated.

Problem $4\mathrm{.}2.(10\%)$ Consider the following piecewise function $y(x).$ Use FOR loops and IF conditional

statements to construct $5$ different $y$ vs$.x$ plots. Each plot will consider a specific value for $a$ in the range $0$

$a<mn>2</mn><mn>0</mn><mtext></mtext><mi>(</mi>$e$.$g$.,a=1,5,9,13,17).$ Display all $5$ plots on the same figure.

$xyx1010$ARATA,$RT$