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

Using Vieta's formulas, k = (-2)(-4) = 8.

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

The sum of the roots is 3 + (-3) = 0, so b = -0.

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

Using Vieta's formulas, m = -(1 + (-3)) = 2.

Using Vieta's formulas, the product of the roots is n = 1 * (-3) = -3.

Using Vieta's formulas, m = -(-1) = 1 and n = 2*(-3) = -6, thus m + n = 1 - 6 = -5.

Using Vieta's formulas, p = -(2 + 3) = -5 and q = 2*3 = 6. Thus, p + q = -5 + 6 = 1.

The sum of the roots is -p = 2 + 3 = 5, so p = -5.

For equal roots, the discriminant must be zero: k^2 - 36 = 0, hence k = 6.

Range = Maximum - Minimum. Therefore, Maximum = Range + Minimum = 15 + 5 = 20.

A relation is reflexive if every element in the set is related to itself. Here, R includes (1, 1), (2, 2), and (3, 3), so R is reflexive.

A relation is reflexive if every element is related to itself. Here, (1,1), (2,2), and (3,3) are not in R, so R is not reflexive.

Using the sum of roots (-b/a = 3 + (-2) = 1), we find b = -1.

Using Vieta's formulas, a = 1 since the product of the roots (3 * -2) = -6 and sum (3 + -2) = 1.

The discriminant must be greater than zero: 4^2 - 4*1*k > 0 => 16 - 4k > 0 => k < 4.

For real and equal roots, the discriminant must be zero: 16 - 4k = 0, thus k = 4.

Using Vieta's formulas, the sum of the roots is -b/a = -5/1 = -5.

Using the sum and product of roots: -2 + -4 = -6 and -2*-4 = k => k = 8.

The sum of the roots is -(-2 - 3) = 5, so m = 5. The product of the roots is (-2)(-3) = 6, so n = 6. Thus, m + n = 5 + 6 = 11.

Using Vieta's formulas, p = -(-2 - 3) = 5.

Using Vieta's formulas, p = -(-2 - 3) = 5 and q = (-2)(-3) = 6. Therefore, p + q = 5 + 6 = 11.

The sum of the roots is 0, hence p = -sum = 0.

For equal roots, the discriminant must be zero: p^2 - 4q = 0, hence p^2 = 4q.

For the roots to be equal, the discriminant must be zero. Thus, b^2 - 4ac = 0 => 25 - 4k = 0 => k = 25.

The minimum value of k is 6, as the discriminant must be zero.

For real and equal roots, the discriminant must be zero: 25 - 4k = 0, thus k = 6.

Using Vieta's formulas, the sum of the roots is 7 and the product is p. Thus, 3 * 4 = p, so p = 12.

Let the roots be 3k and 4k. Then, 3k + 4k = 7 => 7k = 7 => k = 1. The product of the roots is 3k * 4k = 12k^2 = p => p = 12.