Please help solve the following Asset Allocation problem.

You want to assess Sam's risk preference first. You asked Sam the following question: "Suppose you have 100 dollars. There is a cointossing game to play (the coin is fair). For every dollar you put in the game, you will get three dollars back if the head turns up but nothing if the outcome is the tail. How much money would you put in the game?" Sam said that he would put 10 dollars in the game and hold the remaining 90 dollars as cash (i.e., the return rate for these 90 dollars is zero). Determine Sam's risk-aversion index assuming that his utility function is given by the quadratic one