Answer
$x^2-15x+50=0$
Work Step by Step
With the given roots, $
5\text{ and }10
,$ then
\begin{align*}
x&=5
\\\\&\text{ OR }\\\\
x&=10
.\end{align*}
Using the properties of equality, the equations above are equivalent to
\begin{align*}
x&=5
\\
x-5&=0
\\\\&\text{ OR }\\\\
x&=10
\\
x-10&=0
.\end{align*}
A quadratic equation that has the two given roots is
\begin{align*}
(x-5)(x-10)&=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(-10)-5(x)-5(-10)&=0
\\
x^2-10x-5x+50&=0
\\
x^2-15x+50&=0
.\end{align*}
Hence, a quadratic equation that has the given pair of numbers as roots is $
x^2-15x+50=0
$.
