Question

What are the zeros of the function f(x)=-x^2+13x-36

Answer 1

For this case we have the following function:

`f (x) = - x ^ 2 + 13x-36`

To find the zeros of the function we make
`y = 0`and solve for "x", then:

`0 = -x ^ 2 + 13x-36`

We multiply by -1 on both sides of the equation:

`0 = x ^ 2-13x + 36`

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.

`(-9) * (- 4) = 36\\-9-4 = -13`

Thus, the factored equation is:

`(x-9) (x-4) = 0`

Therefore, the roots are:

`x_ {1} = 9\\x_ {2} = 4`

Answer:

`x_ {1} = 9\\x_ {2} = 4`