The product of the roots is given by c/a = 8/1 = 8.

The product of the roots is c/a = 9/1 = 9.

Factoring gives (x + 4)(x - 2) = 0, hence the roots are -4 and 2.

This is a perfect square: (x + 3)² = 0, hence the root is x = -3.

Dividing by 3 gives x² - 4x + 4 = 0, which factors to (x - 2)² = 0, hence the root is 2.

This is a perfect square: (2x - 3)² = 0, hence the root is x = 1.5.

Factoring gives (x + 4)(x - 2) = 0, hence the roots are 4 and -2.

The discriminant must be negative: 4² - 4*1*k < 0, which gives k > 4, so the minimum value is -6.

For equal roots, the discriminant must be zero: k² - 4*1*16 = 0, thus k² = 64, k = ±8. The value of k can be -8.

For no real roots, the discriminant must be negative: k² - 4*1*9 < 0, thus k² < 36, hence k < -6 or k > 6.

For no real roots, the discriminant must be less than zero: k² - 4*1*16 < 0, which gives k > 8.

The discriminant must be non-negative: 4² - 4*1*k ≥ 0, thus k ≤ 4.

The discriminant must be non-negative: 6² - 4*1*k ≥ 0, which gives k ≤ 9, so the minimum value is -9.

The discriminant must be non-negative: 6² - 4*1*k ≥ 0, thus k ≤ 9.

The discriminant must be non-negative: 2² - 4*1*k ≥ 0, which simplifies to k ≤ 1.

The discriminant must be less than zero: 6² - 4*1*k < 0, which simplifies to k > 9.

The discriminant must be non-negative: 6² - 4*1*k ≥ 0, thus k ≤ 9. The minimum value of k is -9.

The discriminant must be less than zero: k² - 4*1*9 < 0, thus k² < 36, so k > 6 or k < -6.

For both roots to be positive, k must be greater than 0 and k² > 4*9 = 36, thus k > 6.

For both roots to be negative, m must be greater than 0 and m² < 36. Thus, m must be in the range (-6, 0). The suitable value is -4.

The sum of the roots is 3 + 3 = 6, hence m = 6.

Using the sum of roots: 2 + (-2) = -p, hence p = 0.

For both roots to be negative, p must be greater than 0 and p² > 16. Thus, p < -4.

For both roots to be negative, p must be positive and p² > 4*9. Thus, p > 6, so p = -4 is valid.

The sum of the roots is 3 + 3 = 6, hence p = 6.

Using the root 2 in the equation: 2² - 6*2 + k = 0, we find k = 10.

Using the root, substitute x = 3: 3² - 7*3 + k = 0, which gives k = 10.

Using the root, substitute x = 3: 3² - 7*3 + k = 0, which gives k = 9.

Using the root, substitute x = 3: 3² - 7*3 + p = 0, which gives p = 6.

The product of the roots gives k = (-2)(-3) = 6.