Use Descartes' Rule of Signs to Determine the Possible Number $f ( x ) = 5 x ^ { 5 } + 10 x$

question 16

Multiple Choice

Use Descartes' Rule of Signs to determine the possible number of positive and nega- tive zeros of $f ( x ) = 5 x ^ { 5 } + 10 x$

• A) 1 positive real; 3 negative reals or 1 negative real
• B) 5 positive reals or 3 positive reals or 1 positive real; no negative reals
• C) no positive reals; no negative reals
• D) 3 positive reals or 1 positive real; 3 negative reals or 1 negative real
• E) 1 positive real; 5 negative reals or 3 negative reals or 1 negative real

---

Definitions:

Binomial Population

A population in which each member of the population has only two possible outcomes or states, often conceptualized as success or failure.

Population Proportion

The fraction or percentage of individuals in a population who possess a particular attribute or characteristic.

Critical Value

A point on the scale of the test statistic beyond which we reject the null hypothesis; it marks the boundary for deciding whether a statistic is significant.

Type II Error

A statistical error occurring when a hypothesis test fails to reject a false null hypothesis.