For this case we have the following function:
[tex]f (x) = - x ^ 2 + 13x-36[/tex]
To find the zeros of the function we make [tex]y = 0[/tex]and solve for "x", then:
[tex]0 = -x ^ 2 + 13x-36[/tex]
We multiply by -1 on both sides of the equation:
[tex]0 = x ^ 2-13x + 36[/tex]
We factor the equation, for this we look for two numbers that, when multiplied, result in 36 and when added, result in -13. These numbers are -9 and -4.
[tex](-9) * (- 4) = 36\\-9-4 = -13[/tex]
Thus, the factored equation is:
[tex](x-9) (x-4) = 0[/tex]
Therefore, the roots are:
[tex]x_ {1} = 9\\x_ {2} = 4[/tex]
Answer:
[tex]x_ {1} = 9\\x_ {2} = 4[/tex]
