What are the possible rational roots of f(x) = 3x4 – x3 + x2 – x + 5?Question 37Select one:a.{±1, ±5}b.{±1/3, ±5/3}c.{±1, ±1/3, ±5, ±5/3}d.{1, 1/5, 3, 3/5}e.{1, 1/3, 5, 5/3}
Question
What are the possible rational roots of f(x) = 3x4 – x3 + x2 – x + 5?Question 37Select one:a.{±1, ±5}b.{±1/3, ±5/3}c.{±1, ±1/3, ±5, ±5/3}d.{1, 1/5, 3, 3/5}e.{1, 1/3, 5, 5/3}
Solution
The possible rational roots of a polynomial can be determined using the Rational Root Theorem. This theorem states that if a polynomial has a rational root p/q (where p and q are relatively prime), then p is a factor of the constant term (in this case, 5) and q is a factor of the leading coefficient (in this case, 3).
The factors of 5 are ±1, ±5 and the factors of 3 are ±1, ±3.
Therefore, the possible rational roots of the polynomial are all combinations of these factors, which are {±1, ±1/3, ±5, ±5/3}.
So, the correct answer is c.{±1, ±1/3, ±5, ±5/3}.
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