Find All Real Zeros of the Polynomial $f ( x ) = x ^ { 4 } - 61 x ^ { 2 } + 900$

question 51

Multiple Choice

Find all real zeros of the polynomial $f ( x ) = x ^ { 4 } - 61 x ^ { 2 } + 900$ and determine the multiplicity of each.

• A) \(x = - 5 , \text { multiplicity } 2 ; x = - 6 , \text { multiplicity } 2\)
• B) \(x = 25 , \text { multiplicity } 2 ; x = 36 \text {, multiplicity } 2\)
• C) \(x = 5 , \text { multiplicity } 2 ; x = 6 , \text { multiplicity } 2\)
• D) \(x = 25 , \text { multiplicity } 2 ; x = 6 , \text { multiplicity } 2\)
• E) \(x = 5 \text {, multiplicity } 1 ; x = - 5 \text {, multiplicity } 1 ; x = 6 \text {, multiplicity } 1 ; x = - 6 \text {, multiplicity } 1\)

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Definitions:

Product Differentiation

The strategy of setting a product or service apart from others in the industry to enhance its attractiveness to a specific target group.

Allocative Efficiency

A condition of distributing resources in which improving the situation of one person necessitates the detriment of another.

Long-Run Equilibrium

A state in which all factors of production can be adjusted, markets clear, and no economic agents have the incentive to change their behavior.

Marginal Revenue

The additional income that a business receives from selling one more unit of a good or service.