What are the roots of the polynomial equation? x^2−12x−64=0

It is a quadratic equation so we can use the quadratic formula to solve it.
x^2−12x−64=0
a = 1
b = -12
c = -64
x = [-b +-sq root (b^2 -4ac)]  / 2a
x = [--12 +- sq root (144 -4*1*-64)] / 2
x = [12 +- 20] / 2
x1 = 16
x2 = -4

Ais the answer for your question