Nested models and residual sums of squares

Model-I: $Y=\beta_0+\beta_1X$ and Model-II: $Y=\beta_0+\beta_1X+\beta_2X^2$ are fitted for the data set $(X_i,Y_i); i=1,2,\dots,n$. Denote $\hat\beta_0$ and $\hat\beta_1$ as least square estimates of $\beta_0,\beta_1$ from Model-I, and $\beta_0^*,\beta_1^*,\beta_2^*$ be the least square estimates from Model-II. Define $P=\sum_{i=1}^n(Y_i-\hat\beta_0-\hat\beta_1X_i)^2$ and $Q=\sum_{i=1}^n(Y_i-\beta_0^*-\beta_1^*X_i-\beta_2^*X_i^2)^2$. Consider the following statements:

I. $P\ge Q$

II. It can happen that $Q=0$ but $P>0$.

Which of the statements given above is/are correct?