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:

Perilymph

The fluid that fills the space between the membranous and bony labyrinths of the inner ear, providing nutrient support and conducting sound waves.

Earlobes

The lower part of the external ear, which is made of soft skin and fatty tissue and hangs down freely.

Fetus

A developing human from roughly eight weeks after conception until birth in mammalian species, particularly humans.

Cochlea

A spiral-shaped cavity in the inner ear that plays a key role in the sense of hearing by converting sound waves into nerve impulses.