Given the polynomial F(x)=2x3-9x2-6x+40, the first potential roots are -2, 4 and 5/2. Solving for the first root, we divide the given function by x+2 where the result is 2x2-13x+40. Since the given polynomial is divisible by x+2, therefore the first root is -2. For the second and third roots of the function, we can solve it using the quadratic equation formula.