Question

The weekly revenue for a company is r=-2p^2+50p+203​, where p is the price of the​ company's product. Use the discriminant to find whether there is a price for which the weekly revenue would be ​$2000

Answer 1

`\Large \textsf{Read below}`

Explanation:

`\Large \text{$ \sf r = -2p^2 + 50p + 203$}`

`\Large \text{$ \sf 2000 = -2p^2 + 50p + 203$}`

`\Large \text{$ \sf -2p^2 + 50p + 203 - 2000 = 0$}`

`\Large \text{$ \sf -2p^2 + 50p - 1797 = 0$}`

`\Large \text{$ \sf 2p^2 - 50p + 1797 = 0$}`

`\Large \boxed{\text{$ \sf a = 2,\: b = -50,\:c = 1797$}}`

`\Large \text{$ \sf \Delta = b^2 - 4.a.c$}`

`\Large \text{$ \sf \Delta = (-50)^2 - (4).(2).(1797)$}`

`\Large \text{$ \sf \Delta = 2500 - 14376$}`

`\Large \text{$ \sf \Delta = -11876$}`

`\Large \text{$ \sf \Delta < 0$}`

`\Large \boxed{\boxed{\textsf{S = \{\}}}}`