Solve the equation exactly in the complex number system.
-The profit function for a product is given by $P ( x ) = - 0.3 x ^ { 3 } + 75 x ^ { 2 } - 2820 x - 36,000$dollars, where x is the number of units produced and sold. If break-even occurs when 60 units are produced and sold, use synthetic division To find a quadratic factor of P(x) and then find a number of units other than 60 that gives break-even for the Product.
A) 250 units
B) 100 units
C) 200 units
D) 10 units

Question

Quizplus · Accepted Answer

Using synthetic division with $x = 60$, we find that the quadratic factor of $P(x)$ is $-0.3x^2 + 57x + 600$. Solving this quadratic equation, we find another root at $x = 200$.

Solve the Equation Exactly in the Complex Number System P(x)=−0.3x3+75x2−2820x−36,000P ( x ) = - 0.3 x ^ { 3 } + 75 x ^ { 2 } - 2820 x - 36,000P(x)=−0.3x3+75x2−2820x−36,000

Solve the Equation Exactly in the Complex Number System $P ( x ) = - 0.3 x ^ { 3 } + 75 x ^ { 2 } - 2820 x - 36,000$