Find the Real Solutions, If Any, of the Equation $$4 x ^ { 2 } - x + 7 = 0$$

question 15

Multiple Choice

Find the real solutions, if any, of the equation. Use the quadratic formula.
- $$4 x ^ { 2 } - x + 7 = 0$$

• A) \(\left\{ \frac { - 1 - \sqrt { 113 } } { 8 } , \frac { 1 + \sqrt { 113 } } { 8 } \right\}\)
• B) \(\left\{ \frac { - 1 + \sqrt { 113 } } { 8 } , \frac { 1 + \sqrt { 113 } } { 8 } \right\}\)
• C) no real solution
• D) \(\left\{ \frac { - 1 - \sqrt { 113 } } { 8 } , \frac { - 1 + \sqrt { 113 } } { 8 } \right\}\)

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Definitions:

Monopoly

A market structure characterized by a single seller who has exclusive control over a product or service, with no close substitutes.

Cournot Model

A model in economic theory that describes an industry structure where companies compete on the basis of quantity produced, leading to a specific equilibrium.

Collusion Laws

refer to regulations aimed at preventing firms or individuals from working together to manipulate prices, limit competition, or engage in other practices deemed unfair or anti-competitive.

Oligopolies

Market structures characterized by a small number of firms dominating the industry, often leading to limited competition and higher prices.