Answer
$\text{sum:}$ $
-\dfrac{2}{5}
$
$\text{product:}$ $
\dfrac{1}{5}$
Work Step by Step
In $ax^2+bx+c=0,$ the sum of the roots is given by $-\dfrac{b}{a}$ while the product of the roots is given by $\dfrac{c}{a}$.
In the given quadratic equation,
\begin{align*}
5x^2+2x+1=0
,\end{align*} $a=
5
,$ $b=
2
,$ and $c=
1
.$ Using the sum and product ratios of quadratic equations, then
\begin{align*}\require{cancel}
\text{Sum: }\\-\dfrac{b}{a}&=-
\dfrac{2}{5}
\\\\
\text{Product: }\\\dfrac{c}{a}&=
\dfrac{1}{5}
.\end{align*}
Hence, $
\text{the sum is }$ $
-\dfrac{2}{5}
$ $\text{ and the product is }$ $
\dfrac{1}{5}
$.