Find All Real Zeros of the Polynomial $p ( x ) = - x ^ { 3 } + 9 x ^ { 2 } - 24 x + 16$

question 117

Essay

Find all real zeros of the polynomial $p ( x ) = - x ^ { 3 } + 9 x ^ { 2 } - 24 x + 16$ . Sketch the graph of $p$ .

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Definitions:

Coefficient

A numerical or constant factor in a mathematical expression, showing the degree of some change under certain conditions, often used in equations to measure relationships between variables.

Price Elasticity of Supply

This measures how much the quantity supplied of a good changes in response to a change in the price of that good.

Midpoint Formula

A method used in economics to calculate the elasticity of a variable, such as demand or supply, based on changes in price and quantity from a midpoint on a curve.

Elastic

Describes a situation in economics where the demand or supply for a good or service significantly changes in response to a change in price.