The discriminant D = b^2 - 4ac = 4^2 - 4(2)(2) = 16 - 16 = 0.

The discriminant is 0, indicating that the roots are real and equal.

For equal roots, the discriminant must be zero: k^2 - 4*1*16 = 0. Solving gives k = -8.

The sum of the roots is 3 + (-1) = 2, hence p = -2.

By Vieta's formulas, the sum of the roots p + q = -b/a.

The equation can be factored as (x + 1)(x + 1) = 0, giving the root -1 with multiplicity 2.

Using Vieta's formulas, k = (-1)(-2) = 2.

The discriminant must be less than zero: (-4)^2 - 4*2*k < 0 leads to k > 8.

This is a perfect square trinomial: (x + 3)(x + 3) = 0.

For both roots to be negative, k must be greater than the square of half the coefficient of x, hence k > 9.

Using Vieta's formulas, the sum of the roots is -b/a = -12/3 = -4.

Using Vieta's formulas, the product of the roots is c/a = 10/1 = 10.