Please help me and show steps! I would really appreciate it!
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1 Answer

1. User Answers elcharly64
Answer:
The aircraft has a height of 1000 m at t=2 sec, and at t=8 sec
Stepbystep explanation:
Finding Exact Roots Of Polynomials
A polynomial can be expressed in the general form
[tex]\displaystyle p(x)=a_nx^n+a_{n1}\ x^{n1}+...+a_1\ x+a_0}[/tex]
The roots of the polynomial are the values of x for which
[tex]P(x)=0[/tex]
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
[tex]\displaystyle h(x)=0.5(t^4+10t^3216t^2+2000t1200)[/tex]
We need to find the values of t that make H=1000, that is
[tex]\displaystyle 0.5(t^4+10t^3216t^2+2000t1200)=1000[/tex]
Dividing by 0.5
[tex]\displaystyle t^410t^3+216t^22000t+1200=2000[/tex]
Rearranging, we set up the equation to solve
[tex]\displaystyle t^410t^3+216t^22000t+3200=0[/tex]
Expanding some terms
[tex]\displaystyle t^48t^32t^3+200t^2+16t^21600t400t+3200=0[/tex]
Rearranging
[tex]\displaystyle t^48t^3+200t^21600t2t^3+16t^2400t+3200=0[/tex]
Factoring
[tex]\displaystyle t(t^38t^2+200t1600)2(t^38t^2+200t1600)=0[/tex]
[tex]\displaystyle (t2)(t^38t^2+200t1600)=0[/tex]
This produces our first root t=2. Now let's factor the remaining polynomial
[tex]\displaystyle t^2(t8)+200(t8)=0[/tex]
[tex]\displaystyle (t^2+200)(t8)=0[/tex]
This gives us the second real root t=8. The other two roots are not real numbers, so we only keep two solutions
[tex]\displaystyle t=2,\ t=8[/tex]