answer this question below

Consider the utility function: U(w) = a + bw + cw2. (a) What restrictions must be placed on a, b, and c for this function to display risk aversion? (b) State the domain of wealth, w, where the utility function can be defined properly. (c) Given the gamble: g [( ) . ( W + 1) . ( 2 ). (w- show that the certainty equivalent is less than the expected value of the gamble, and that the risk premium is strictly positive. (d) Show that if the restrictions in part (a) are satisfied, then this utility function does not represent preferences that display decreasing absolute risk aversion