According to the discriminant of the quadratic equation, it will have equal roots for p = -16.
A quadratic equation is modeled by:
[tex]y = ax^2 + bx + c[/tex]
The discriminant is:
[tex]\Delta = b^2 - 4ac[/tex]
The solutions are as follows:
In this problem, the equation is:
[tex]f(x) = -x^2 + 8x + p[/tex]
Hence the coefficients are a = -1, b = 8, c = p.
It has equal roots if [tex]\Delta = 0[/tex], hence:
[tex]b^2 - 4ac = 0[/tex]
[tex]8^2 + 4p = 0[/tex]
[tex]4p = -64[/tex]
[tex]p = -16[/tex]
More can be learned about the discriminant of a quadratic equation at https://brainly.com/question/19776811