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

question 393

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:

Contribution Margin Mix

The relative proportion of different products or services, contributing to the total contribution margin, highlighting how combination effects overall profitability.

Break-Even Point

The point at which total costs and total revenue are equal, meaning there is no net loss or gain, and one has 'broken even'.

Unit Contribution Margins

The difference between the selling price per unit and variable cost per unit, indicating the contribution of each unit sold to covering fixed costs.

Fixed Costs

Expenses that do not change with the level of production or sales activities within a certain range or period.