an ant has fallen into a bottle 60cm deep and is climbing up 8 cm everyday. As it is exhausted, the ant is slipping down 4cm every night. Then how long would it take teh ant to escape from the bottle

It took 13 days and a half to escape

Step-by-step explanation:

This is a classic problem where the first answer that comes to one's mind is not the correct answer.

The ant climbs up 8 cm per day and slips down 4 cm every night. It means the real distance the ant goes up is 8 - 4 = 4 cm per day. Since the total distance is 60 cm, it could lead us to think the time needed to escape from the bottle is 60/4=15 days. This is wrong, as we'll prove below.

Assume the last day, the ant climbs up the final 8 cm and escapes. We don't know yet when, but we can assure that day the ant was at a height of 60 - 8 = 52 cm.

That 52 cm was the result of the 4 cm per day the ant effectively went up, thus it needed 52/4=13 days to reach that height.

At 13 days, the ant was at 52 cm, the day 14 it climbed up the final 8 cm and escaped.

It took 13 days and a half to escape

f(x) = x^3 -2x^2 -3x

x( x^2 -2x-3)

x( x^2 +x -3x -3)

x( x(x+1) -3(x+1))

x( x-3)( x+1)

so zeroes are 0, 3,-1

its (2) option