# Help on tis quadratic functions question

1. Oct 20, 2007

### fluffy91

[SOLVED] Help on tis quadratic functions question

1. The problem statement, all variables and given/known data
The speed v m/s of a particle travelling from A to B at time t s after leaving A, is given by v =10t-t². the particle starts from rest at A and comes to rest at B. Show that the particle has a speed of 5m/s or greater for exactly 4$$\sqrt{5}$$ s

2. Relevant equations
NOne

3. The attempt at a solution

10t-t²>5
t²-10t+5 <0
0.52 < t < 9.47
then i dunno how to do already.
Can someone start me off and guide me along?

2. Oct 20, 2007

### danago

3. Oct 20, 2007

### arildno

Sigh. You have already solved the problem, but because you are so infatuated with decimal approximations, you don't see the answer even when it stares you in the eye.

On your second line, we factorize the quadratic, with the two zeroes:
$$X=\frac{-(-10)\pm\sqrt{(-10)^{2}-4*1*5}}{2*1}=\frac{10\pm\sqrt{80}}{2}=\frac{10\pm\sqrt{16*5}}{2}=5\pm{2}\sqrt{5}$$

You have found that the relevant region lies between these 2 zeroes, and we may then calculate the distance between them:
$$(5+2\sqrt{5})-(5-2\sqrt{5})=4\sqrt{5}$$
as was to be shown.