Question

the profit made when t units are sold, t > 0, is given by P=t^2-36t+320. Determine the number of units in order for P > 0 (a profit is made).

Answer 1

P=t^2-36t+320>0

for zeroes, t=(36+-4)/2=20;16

well, if those are the zeroes, then between them are the P<0

example, t=18
P=18^2-36*18+320=320-18^2=-4

example, t=22, P=22^2-36*22+320
P=12

Answer 2

(t-20)(t+16) = 0
t = 20 is positive root
parabola opens up, anything above right hand root is positive p
so
t>20

Answer 3

(t-20)(t-16) = 0
t = 20 is right hand root