Question

Which lists the possible types of roots for

f
(
x
)
=
3
x
4
+
7
x
3
+
2
x
2
+
x
+
9
?

Answer 1

Answer: ±1, ±3, ±9, ±
`(1)/(3)`

Explanation:

f(x)=3x⁴+7x³+2x²+9

To find all possible roots, you take the last number and all its factors and put it over the first number and all its factors.

Factors of last and first:

9: 1, 3, 9

3: 1, 3

Put all of the factors of 9 divided by all factors of 3 and also make them + and - versions. Also eliminate any repeats like ±
`(1)/(1)` and ±
`(3)/(3)`

±1, ±3, ±9, ±
`(1)/(3)`

Answer 2

Please provide more details!

To determine the specific type of roots for the given quartic equation, we need to solve it or analyze its discriminant. However, without further calculations, we cannot determine the exact types of roots for f(x) = 3x^4 + 7x^3 + 2x^2 + x + 9.