Answer:
[tex]\displaystyle five\:seconds[/tex]
Step-by-step 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:
[tex]\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][/tex]
Set the factors equal to zero to determine the time:
[tex]\displaystyle 0 = [t - 5][5t + 2] \\ \\ -\frac{2}{5}, 5 = t[/tex]
*Time is NEVER negative, therefore it will take five seconds for the rocket to hit the ground.
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