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The aircraft has a height of 1000 m at t=2 sec, and at t=8 sec

Step-by-step explanation:

Finding Exact Roots Of Polynomials

A polynomial can be expressed in the general form    

The roots of the polynomial are the values of x for which    

Finding the roots is not an easy task and trying to find a general solution has been discussed for centuries. One of the best possible approaches is trying to factor the polynomial. It requires a good eye and experience, but it gives excellent results.    

The function for the trajectory of an aircraft is given by    

We need to find the values of t that make H=1000, that is

Dividing by -0.5

Rearranging, we set up the equation to solve

Expanding some terms

Rearranging

Factoring

This produces our first root t=2. Now let's factor the remaining polynomial

This gives us the second real root t=8. The other two roots are not real numbers, so we only keep two solutions

answer: what are the following choices