9. 8. On the blackboard, there are $n$ expressions of the form $* x^{2}+* x+* =0$ ($n$ is odd). Two people take turns playing a game, each step allowing the replacement of one “star” with a number not equal to 0. After $3 n$ steps, $n$ quadratic equations are obtained. The first person aims to make as many equations as possible have no roots, while the second person tries to prevent the first person from achieving his goal. Question: What is the maximum number of rootless equations the first person can get, regardless of what the second person does?
9. 8. $\frac{n+1}{2}$. process of the same kind.

Now, the first use of a number to replace the "star" in the expression is called breaking down the expression. The first player's first step should be to break down one of the expressions in their expression and fill in the number 1 before $x$. If the second player fills in the number $a$ before $x^{2}$, or replaces the constant term with $a$, then the first player fills in the number $\frac{1}{a}$ in the remaining positions. Thus, the discriminant of the resulting equation $\Delta=1-4 a \cdot \frac{1}{a}=-3$, so the equation has no roots. If the second player replaces one of the "stars" in the expression he previously broke down with a number, then the first player can arbitrarily fill in the remaining positions in this expression. Clearly, the above strategy allows the first player to break down $\frac{n+1}{2}$ expressions, and these expressions are transformed into equations without roots by the first player.

It also needs to be proven that the second player, while preventing the first player, can also obtain $\frac{n-1}{2}$ equations with roots. In fact, the second player can break down expressions $\frac{n-1}{2}$ times and fill in the number 1 before $x^{2}$. Then, no matter what the first player does, the second player can always fill in a number in each of the expressions he breaks down. If the constant term has not been filled with a number, the second player fills in the number -1 in this position, ensuring an equation with a discriminant greater than zero. If the first player fills in the number $c$ in the constant term position, then the second player just needs to fill in the number $b>2 \sqrt{|c|}$ before $x$, which will suffice.