The product of the roots is (-2)(-3) = 6, so k = 6.

Using the product of roots, k = 1*4 = 4.

The discriminant must be greater than zero: 5^2 - 4(1)(k) > 0, leading to k < 25.

The equation can be factored as (x+3)(x+3)=0, hence the root is -3.

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

For real and distinct roots, the discriminant must be greater than zero: 6^2 - 4*1*k > 0 leads to k < 9.

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, n = 3 * 4 = 12.

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.

Using the sum of roots formula, p = -(4 + (-1)) = -3.

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

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

The product of the roots is 5*5 = 25, hence k = 25.

The discriminant must be positive for real and distinct roots: (-2)^2 - 4*1*k > 0, which simplifies to 4 - 4k > 0, or k < 1.

The discriminant must be greater than zero for real and distinct roots: (-4)^2 - 4*1*k > 0, which simplifies to 16 - 4k > 0, or k < 4.

According to Vieta's formulas, the sum of the roots p + q is equal to -(-5) = 5.

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, k = 2 * 4 = 8.

The equation can be expressed as (x - 3)^2 = 0, which expands to x^2 - 6x + 9 = 0. Thus, k = 9.

For real and distinct roots, the discriminant must be greater than zero: (-6)^2 - 4*1*k > 0, leading to k < 9.

By Vieta's formulas, ab = 10, which is the constant term of the polynomial.

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.

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

Using the sum and product of roots: 1 + (-3) = -2 and 1 * (-3) = -3, thus k = 3.

The discriminant must be greater than zero: 2² - 4*1*k > 0, which simplifies to k < 1.