Answer
$a=1, b=-9, \text { and } c=20$
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 $\{
4,5
\},$ is
\begin{array}{l}\require{cancel}
(x-4)(x-5)=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(-5)-4(x)-4(-5)=0
\\\\
x^2-5x-4x+20=0
\\\\
x^2-9x+20=0
.\end{array}
Hence, $
a=1, b=-9, \text { and } c=20
.$
