The roots of the equation 2x^2-2x-60=0 have to be determined to see if they are integers.

2x^2-2x-60=0

2 is a common factor and can be factored out

x^2 - x - 30 = 0

x^2 - 6x + 5x - 30 = 0

x(x - 6) + 5(x - 6) = 0

(x + 5)(x - 6) = 0

x = -5 and x = 6

The roots of the equation 2x^2-2x-60=0 are integers and they are x = -5 and x = 6

To check the nature of the roots of the quadratic, we'll have to solve the equation. First, we'll divide the equation by 2:

x^2 - x - 30 = 0

We'll verify if the equation has any roots.

For this reason, we'll determine the discriminant of the quadratic:

delta = b^2 - 4ac

a,b,c, are the coefficients of the equation:

a = 1, b = -1 and c = -30

delta = 1 + 120

delta = 121

Since delta is positive, the quadratic has 2 different roots.

Now, we'll apply quadratic formula to determine the roots of the equation:

x1 = (1 + sqrt121)/2

x1 = (1+11)/2

x1 = 12/2

x1 = 6

x2 = (1-11)/2

x2 = -10/2

x2 = -5

**We notice that both roots of the quadratic are integer and they are: x1 = 6 and x2 = -5.**