Question

Using the rational root theorem, list out all possible/candidate rational roots of

f(x)=3x⁵+12x⁴+24x³+2x²+28x+17.
Express your answer as integers or as fractions in simplest form. Use commas to separate.

Answer 1

The possible rational roots of the polynomial f(x)=3x⁵+12x⁴+24x³+2x²+28x+17 are ±1, -1, ±17, -17, ±1/3, -1/3, ±17/3, and -17/3. They are determined by dividing the factors of the constant term by the factors of the leading coefficient.

Step-by-step explanation:

The rational root theorem can be used to list all possible rational roots for the polynomial f(x) = 3x⁵ + 12x⁴ + 24x³ + 2x² + 28x + 17. To find the possible roots using this theorem, you take the factors of the constant term (17) and divide them by the factors of the leading coefficient (3). The factors of 17 are ±1, ±17, and the factors of 3 are ±1, ±3. This gives us a list of potential rational roots:

• ±1, -1, ±17, -17
• ±1/3, -1/3, ±17/3, -17/3

These roots should be checked for validity by substituting them into the polynomial to see if they yield a zero value.