Use Descartes' Rule of Signs to Determine the Possible Number $f ( x ) = x ^ { 5 } + x ^ { 4 } + x ^ { 2 } + x + 7$

question 130

Multiple Choice

Use Descartes' Rule of Signs to determine the possible number of positive and negative real zeros for the polynomial
function.
- $f ( x ) = x ^ { 5 } + x ^ { 4 } + x ^ { 2 } + x + 7$

• A)0 positive zeros, 1 negative zero
• B)0 positive zeros, 0 negative zeros
• C)0 positive zeros, 2 or 0 negative zeros
• D)0 positive zeros, 3 or 1 negative zeros

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Definitions:

Cationic

Refers to species (typically ions) that have a net positive charge.

Teflon

A synthetic fluoropolymer of tetrafluoroethylene that has numerous applications, known for its non-reactivity and ability to withstand high temperatures.

Poly(methyl α-cyanoacrylate)

A type of cyanoacrylate polymer that is used as a powerful adhesive in various applications, known commonly as super glue.

Radical Addition

This refers to a chemical reaction wherein radicals (atoms, molecules, or ions with unpaired electrons) are added to other molecules, often leading to polymerization or other significant transformations.