The voltage v$($t$)$ in a network is defined by the equation below, given a $=2,$ b $=5,$ and c $=8.$

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Simplify the given equation to the characteristic equation. What is the $"$q$"$ in the characteristic equation of the network in the form s$2+$ qs $+$ r $?$

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Notes on the solution:

give the answer to $2$ decimal places

example. If the characteristic equation is $5$s$2+7$s $+9$ the solution is entered as $7$

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Group of answer choices

$1\mathrm{.}155$ e$^(-2\mathrm{.}5$t$)$cos$(4\mathrm{.}33$t$)$ V$,$ t$>0$

$1\mathrm{.}155$ e$^(-2\mathrm{.}5$t$)$sin$(4\mathrm{.}33$t$)$ V$,$ t$>0$

$1\mathrm{.}155$ e$^(-2\mathrm{.}5$t$)$ V$,$ t$>0$

$1\mathrm{.}155$ te$^(-2\mathrm{.}5$t$)$ V$,$ t$>0$