Answer
$x^2-16=0$
Work Step by Step
With the given roots, $
-4\text{ and }4
,$ then
\begin{align*}
x&=-4
\\\\&\text{ OR }\\\\
x&=4
.\end{align*}
Using the properties of equality, the equations above are equivalent to
\begin{align*}
x&=-4
\\
x+4&=0
\\\\&\text{ OR }\\\\
x&=4
\\
x-4&=0
.\end{align*}
A quadratic equation that has the two given roots is
\begin{align*}
(x+4)(x-4)&=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(-4)+4(x)+4(-4)&=0
\\
x^2-4x+4x-16&=0
\\
x^2-16&=0
.\end{align*}
Hence, a quadratic equation that has the given pair of numbers as roots is $
x^2-16=0
$.
