Answer
$\text{sum:}$ $
\dfrac{3}{2}
$
$\text{product:}$ $
\dfrac{3}{2}$
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*}
-2x^2+3x-3=0
,\end{align*} $a=
-2
,$ $b=
3
,$ and $c=
-3
.$ Using the sum and product ratios of quadratic equations, then
\begin{align*}\require{cancel}
\text{Sum: }\\-\dfrac{b}{a}&=-
\dfrac{3}{-2}
\\&=
\dfrac{3}{2}
\\\\
\text{Product: }\\\dfrac{c}{a}&=
\dfrac{-3}{-2}
\\&=
\dfrac{3}{2}
.\end{align*}
Hence, $
\text{the sum is }$ $
\dfrac{3}{2}
$ $\text{ and the product is }$ $
\dfrac{3}{2}
$.
