Final answer:
The question likely refers to finding the roots of a quadratic equation using the quadratic formula. The statement about setting the derivative equal to zero doesn't apply when solving for the roots of a quadratic equation, and the result involving 0 < b < 80^3 seems to be unrelated to the typical procedure of applying the quadratic formula.
Step-by-step explanation:
The student's question likely refers to the process of finding the roots of a quadratic equation, which is typically presented in the form ax2 + bx + c = 0. Setting the derivative of a function to zero and solving for a variable such as b is a way to find the extrema of the function, but this doesn't apply directly to solving a quadratic equation for its roots. If we have a quadratic equation with constants a = 1.00, b = 10.0, and c = -200, the roots are found using the quadratic formula, which is √b2 - 4ac over 2a.
However, this process has no bounds on the variable b unless they are specified as conditions for a particular scenario and would not lead to a relationship that is 0 < b < 803. It seems there might be some confusion in the information provided by the student. For a quadratic equation, you are not setting the derivative to zero but rather applying the quadratic formula directly to the equation.