Answer
$a=1, b=1, \text { and } c=-6$
Work Step by Step
$\bf{\text{Solution Outline:}}$
Use the fact that a quadratic equation with roots $r_1$ and $r_2$ has a factored form of $(x-r_1)(x-r_2)=0$. Then use the FOIL Method to convert the equation in the form $ax^2+bx+c=0.$
$\bf{\text{Solution Details:}}$
The factored form of the quadratic equation with the given roots $\{ -3,2 \},$ is \begin{array}{l}\require{cancel} (x-(-3))(x-2)=0 \\\\ (x+3)(x-2)=0 .\end{array}
Using the FOIL Method which is given by $(a+b)(c+d)=ac+ad+bc+bd,$ the expression above is equivalent to\begin{array}{l}\require{cancel} x(x)+x(-2)+3(x)+3(-2)=0 \\\\ x^2-2x+3x-6=0 \\\\ x^2+x-6=0 .\end{array}
Hence, $ a=1, b=1, \text { and } c=-6 .$
