Answer
$x^2-8x+15=0$
Work Step by Step
With the given roots, $
5\text{ and }3
,$ then the factored form of a quadratic equation in $x$ with the given roots is
\begin{align*}
(x-5)(x-3)&=0
.\end{align*}
Using $(a+b)(c+d)=ac+ad+bc+bd$ or the FOIL method, the equation above is equivalent to
\begin{align*}
x(x)+x(-3)-5(x)-5(-3)&=0
\\
x^2-3x-5x+15&=0
\\
x^2-8x+15&=0
.\end{align*}
Hence, a quadratic equation that has the given pair of numbers as roots is $
x^2-8x+15=0
$.
