Solve Word Problem by Using the Discriminent

Question

So I have this math problem

"A model of the daily profits p of a gas station based on the price per gallon g is p = -15,000g² + 34,500g - 16,800. Use the discriminant to find whether the station can profit $4000 per day. Explain."

and the answer key says "No, when p = 4000, the discriminant is negative, so there are no real solutions"

I have no idea how to get that answer and I have a test at 10am. Can someone please help me? Thank you!

Answer 1

Transpose the 4000 so that you have a quadratic equation = 0.

If the quadratic is represented by Ag² + Bg +C,

the discriminant is B² - 4AC, which as you answer says is a negative number.

When the discriminant is negative, the solution contains the square root of a negative number, i.e. the solution is complex, i.e. the 2 roots are NOT real and therefore, the gas station cannot make that profit.