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

question 114

Multiple Choice

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

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Definitions:

Slope

In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line.

Least-Squares Equation

A mathematical method used to find the best-fitting curve to a set of data points by minimizing the sum of the squares of the offsets ("the residuals") of the points from the curve.

House Prices

The prices at which individual houses are bought and sold in the real estate market.

Number Of Rooms

Typically refers to the count of rooms in a building or designated space, often used in real estate and accommodation descriptions.