For both roots to be negative, k must be less than -8 (sum of roots < 0).

For equal roots, D = 0; thus, 6^2 - 4*1*k = 0 => 36 - 4k = 0 => k = 9.

Substituting x = 1 gives 1^2 + 2*1 + k = 0 => 1 + 2 + k = 0 => k = -3.

Using the sum of roots formula, p = -(4 + (-2)) = -2.

The sum of the roots a + b = -(-7) = 7.

The roots can be found using the factorization method: (x-2)(x-3) = 0, hence x = 2 and x = 3.

The product of the roots = c/a = 9/3 = 3.

The sum of the roots = -(-20)/5 = 4.

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

The vertex is at x = -b/(2a) = 4/2 = 2; substituting x = 2 gives y = 2^2 - 4*2 + 3 = -1.