Use Descartesʹ Rule of Signs to Determine the Possible Number $$2 x ^ { 6 } - 3 x ^ { 4 } - 8 x ^ { 3 } + 6 x ^ { 2 } - 3 x = 0$$

question 399

Multiple Choice

Use Descartesʹ Rule of Signs to determine the possible number of positive real zeros and the possible negative real zeros for the function.
- $$2 x ^ { 6 } - 3 x ^ { 4 } - 8 x ^ { 3 } + 6 x ^ { 2 } - 3 x = 0$$

• A) Positive \(( 2,0 )\), negative \(( 3,1 )\)
• B) Positive \(( 3,1 )\), negative \(( 2,0 )\)
• C) Positive \(( 3,1 )\), negative (2)
• D) Positive \(( 2,0 )\), negative \(( 0 )\)

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Definitions:

Deductive Argument

A type of logic where specific conclusions are drawn from general principles or premises, with the conclusion necessarily following from the premises.

Deductive Argument

A logical process in which a conclusion follows necessarily from the given premises.

Valid

A deductive argument where the form is such that the conclusion must be true if the premises are assumed to be true.

Premises

Statements or propositions from which a conclusion is drawn in an argument, assumed to be true.