Question

How do I solve this question?

Answer 1

The correct answer is given by option a.

Explanation:

Rational roots theorem:

In the rational roots theorem, we take the leading coefficient(which multiplies the term of x with the highest exponent) and the independent term(which does not multiply any value of x).

The possible roots have the format p/q, in which p are the factors of the independent term, and q are the factors of the leading coefficient.

In this question:

Leading coefficient: 3

Independent term: 15

Factors of the independent term: {1, 3, 5, 15} -> p

Factors of the leading coefficient: {1,3} -> q

Possible roots:

All possible values, positive or negative, in which p is divided by q. So

`\pm (1)/(1), \pm (1)/(3), \pm (3)/(1), \pm (3)/(3), \pm (5)/(1), \pm (5)/(3), \pm (15)/(1), \pm (15)/(3)`

So, without the repeated terms, they are:

`\pm (1)/(3), \pm (5)/(3), \pm 1, \pm 3, \pm 5, \pm 15`

The correct answer is given by option a.