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**Hint:**Zeros of a polynomial can be defined as the points where the polynomial becomes zero as a whole. A polynomial having value zero (0) is called zero polynomial. To find the zeros of the given polynomial equate it to zero. The degree of a polynomial is the highest power of the variable x.

**Complete step by step answer:**

In the given problem, we have, our polynomial, \[p(x) = 3x + 1\]

So, to find the zeros of the equation, we will equate it to zero,

Thus we get, \[3x + 1 = 0\]

\[ \Rightarrow 3x = - 1\]

On simplifying we get,

\[ \Rightarrow x = \dfrac{{ - 1}}{3}\]

So, a zero of the polynomial is \[ = \dfrac{{ - 1}}{3}\]

**Note:**We can verify the result by substituting it in the given polynomial. For a polynomial, there could be some values of the variable for which the polynomial will be zero. These values are called zeros of a polynomial. Sometimes, they are also referred to as roots of the polynomials. In general, we find the zeros of quadratic equations, to get the solutions for the given equation.

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