Question

Please answer this with explanation and a step-by-step. This is grade 10 math, factoring trinomials complex.

Answer 1

`\displaystyle five\:seconds`

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:

Set the factors equal to zero to determine the time:

*Time is NEVER negative, therefore it will take five seconds for the rocket to hit the ground.

I am joyous to assist you at any time.

Answer 2

Formula in factored form: 0= (5t+2)(t-5)

When the rocket will fall to the ground: 5 seconds

Explanation:

We need to find when the rocket hits the ground given the quadratic formula.

What would be the height of the rocket when it hits the ground? The height would be 0 meters, where it touches the ground. Now set the formula equal to 0. We are solving for t, which is the time it will take in this context to hit the ground.

0= -5t^2+23t+10

What numbers multiply out to -50 and add to the middle term 23?

Those are factor pairs are 25, -2: 25-2= 23, 25*-2=-50

Now we can factor by grouping

0= -5t^2+25t-2t+10

0= (5t+2)(t-5) <--- take out GCF and simplify down

5t+2=0 , t-5=0 <---- Zero product property

Simplify and get t= -2/5, t=5

t= -2/5 is an extraneous solution. You cant have a negative time. If you were to plot this on a graphing calculator you would notice the graph hits the x-axis 2 times (2 roots/zeros). t=5 is the only reasonable root

Thus it will take 5 seconds for the rocket to fall toward the ground.