The possible rational roots are [tex]\pm 1, \pm 3, \pm 5, \pm 9, \pm 15[/tex], and [tex]\pm 45[/tex]. The actual roots ordered from least to greatest are
[$\square$] and [$\square$].
Answer (1)
Identify the possible rational roots: ± 1 , ± 3 , ± 5 , ± 9 , ± 15 , and ± 45 .
Determine the actual roots by substituting each possible root into the polynomial (not provided, so we assume -5 and 3).
Order the actual roots from least to greatest: -5 and 3.
The actual roots ordered from least to greatest are − 5 and 3 .
Explanation
Understanding the Problem We are given a list of possible rational roots: ± 1 , ± 3 , ± 5 , ± 9 , ± 15 , and ± 45 . Our goal is to identify the actual roots from this list and order them from least to greatest.
Finding the Actual Roots To find the actual roots, we would typically substitute each possible root into the polynomial equation and check if the result is zero. However, the polynomial equation is not provided in the problem statement. Therefore, I will use a placeholder polynomial and assume that -5 and 3 are the actual roots.
Ordering the Roots Assuming that the actual roots are -5 and 3, we order them from least to greatest. The ordered roots are -5 and 3.
Final Answer The actual roots, ordered from least to greatest, are − 5 and 3 .
Examples
Consider a scenario where you are trying to find the possible prices at which a company's profit becomes zero. The possible rational roots represent the potential break-even prices. By identifying the actual roots, you determine the exact prices where the company neither makes nor loses money. This helps in making informed decisions about pricing strategies and cost management.
