If I recall correctly, it has something to do with a constant called Jensen's alpha and the extension to something called a multi-factor model.
During my classes (and also wikipedia), the CAPM was stated as follows:
\begin{align}
\mathbb{E}[R_i] = R_{f} + \hat{\beta_{1}}(\mathbb{E}[R_{m}] - R_{f})
\end{align}
When taking excess returns, one would simply have:
\begin{align}
\mathbb{E}[R_i] - R_{f} = \hat{\beta_{1}}(\mathbb{E}[R_{m}] - R_{f})
\end{align}
And this is mostly fine. However, this relation assumes that all information can be taken from just the market portfolio in excess to the risk free rate (i.e. $\hat{\beta_0} =0$). However, it could be the case that your specific return $R_i$ could deviate from the returns seen on the market portfolio. In this case, let us add a constant $\beta_0$ to the model, so we have:
\begin{align}
R_i - R_f= \beta_0 + \beta_{1}(R_{m} - R_{f}) + \epsilon
\end{align}
and when taking expectations
\begin{align}
\mathbb{E}[R_i] - R_{f} =\hat{\beta_0}+ \hat{\beta_{1}}(\mathbb{E}[R_{m}] - R_{f})
\end{align}
Now, suppose you calculate the estimates of $\hat{\beta_0} , \hat{\beta_1}$ using OLS. You will thus now have 2 estimates for the parameters. The way you will generally use the $\hat{\beta_0}$ is by performing a simple t-test test on it:
1: Before testing you have to make sure that the standard errors are correct. Note that the t-test relies directly on the standard errors being homoskedastic, so keep in mind that you will probably have to use robust standard errors, such as Eicker-Huber-White or Newey-West.
2: After you made sure the standard errors from your regression equation are in order you can simply look at the individual t-test for $\hat{\beta_0}$. On the basis of the hypothesis of
\begin{align}
H_0 : \beta_0 = 0 \quad vs \quad H1: \beta_0 \ne 0
\end{align}
On the basis of rejecting the null-hypothesis or failing to reject it, we can distinguish between three cases.
1: $\hat{\beta_0} =0$. In this case, your expected return $\mathbb{E}[R_i] - R_f$ neither outperforms or under performs with respect to the market (which is what your homework is assuming here).
2:$\hat{\beta_0} > 0$. Here, your return is outperforming the market. In this case, the market portfolio can not fully explain your return and additional factors are needed (three-factor model or multi factor models).
3:$\hat{\beta_0}< 0$ . Same as above, only this time the return is under performing with respect to the market portfolio.
All in all, whether or not to include this term depends on whether you assume that no additional factors are needed. If the question states that $R_i$ can be completely explained by just the market portfolio you can simply set this term to zero. In practice, you would perform a statistical hypothesis to test whether it is significantly different from zero or not (Jensen's alpha).
