Whats the answer to this problem?(qudratic equation)?

Question

A water rocket is launched from a platform. The relationship of the height of the rocket from the platform, h, and time, t, is h=-2t^2+3t+2. When will the rocket hit the platform?

Answer 1

The height of the rocket from the platform h = -2t² + 3t + 2.

Now we need to calculate time at which the rocket reaches the platform.

At the Platform the height is equal to 0.

-2t² + 3t + 2 = 0

2t² - 3t - 2 = 0

2t² - 4t + t - 2 = 0

2t(t - 2) + 1(t - 2) = 0

(t - 2) ( 2t + 1) = 0

t = 2 , -0.5

As time cannot be a negative value, then t = 2 sec

Time taken to hit the platform is 2 sec.