To find the zeros of the function \( f(x) = -x^2 + 9x - 20 \), we need to solve the equation:
\[ -x^2 + 9x - 20 = 0 \]
We can multiply through by -1 to simplify it:
\[ x^2 - 9x + 20 = 0 \]
Next, we can factor the quadratic:
\[ (x - 4)(x - 5) = 0 \]
Setting each factor to zero gives us the solutions:
\[ x - 4 = 0 \quad \Rightarrow \quad x = 4 \] \[ x - 5 = 0 \quad \Rightarrow \quad x = 5 \]
Thus, the zeros of the function are \( x = 4 \) and \( x = 5 \).
Now you can fill in the blanks:
- Blank space 1: 4
- Blank space 2: 5
So the final answer is:
\[ x = 4 \quad \text{and} \quad x = 5 \]