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.

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 less than zero: k² - 4*1*16 < 0, which gives k > 8.

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 minimum value of k is -9.

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.

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 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.

Using the product of roots: k = (-2)(-3) = 6.

Using the sum and product of roots: k = 1*4 = 4, and sum = 1 + 4 = 5, thus k = 7.

Using the sum of roots (-3 + -4 = -7) and product of roots (-3*-4 = 12), we find p = 12.

Using the sum of the roots: p = -(3 + 4) = -7.

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

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

The discriminant is b² - 4ac = (-12)² - 4*3*12 = 144 - 144 = 0.

The discriminant is b² - 4ac = (-12)² - 4*3*9 = 0.

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

The product of the roots is given by c/a = 6/1 = 6.

The product of the roots is given by c/a = 24/1 = 24.

The product of the roots is given by c/a = 15/1 = 15.

The sum of the roots is given by -b/a = 4/2 = 2.

The product of the roots is k = 2 * 4 = 8.