Answer:
![\displaystyle five\:seconds](https://img.qammunity.org/2023/formulas/mathematics/high-school/vtyahuk4h9algfwuokbd1wfz524bnvzuqw.png)
Explanation:
Factour this trinomial. Now, as you can see, there is a negative inserted in front of the trinomial. If you are afraid of negatives, easily factour it out and begin the factorisation process:
![\displaystyle -5t^2 + 23t + 10 \hookrightarrow 5t^2 - 23t - 10 \\ \\ [5t^2 - 25t] + [2t - 10] \\ 5t[t - 5]\:\:2[t - 5] \\ \\ [t - 5][5t + 2]]()
Set the factors equal to zero to determine the time:
![\displaystyle 0 = [t - 5][5t + 2] \\ \\ -(2)/(5), 5 = t](https://img.qammunity.org/2023/formulas/mathematics/high-school/lglxvuwsgp19fapx72kneu07fhr9zkky8f.png)
*Time is NEVER negative, therefore it will take five seconds for the rocket to hit the ground.
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