##### Item1.4.4.7.d

Rather than looking for a degree three polynomial, suppose we wanted to find a polynomial that passes through the four points and that has degree two, such as

\begin{equation*} p(x) = a + bx + cx^2 \text{.} \end{equation*}Solve the system of equations for the coefficients. What can you say about the existence and uniqueness of the solutions?