Question

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

f (x) = 4x³ + 10x² + 14x+ 6.
Express your answer as integers or as fractions in simplest form. Use commas to separate.

Answer 1

The possible rational roots of the given polynomial equation are provided using the rational root theorem.

Step-by-step explanation:

The rational root theorem states that if a polynomial equation has a rational root, it can be expressed as a quotient of two integers: p/q, where p is a factor of the constant term and q is a factor of the leading coefficient.

In the given equation f(x) = 4x³ + 10x² + 14x + 6, the constant term is 6 and the leading coefficient is 4. The factors of 6 are ±1, ±2, ±3, and ±6, and the factors of 4 are ±1 and ±4. Therefore, the possible rational roots are:

1. ±1/1
2. ±2/1
3. ±3/1
4. ±6/1
5. ±1/4
6. ±2/4
7. ±3/4
8. ±6/4