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.

The sum of the roots is given by -b/a = -5/1 = -5.

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.

The discriminant must be greater than zero: 5² - 4*1*k > 0, thus k < 25.

Using the product of roots: q = 1 * 4 = 4.

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

Using the product of roots, k = 1*6 = 6.

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

Using the product of roots: p = (-3)(-4) = 12.

Using the product of roots: p = (-3)(-4) = 12.

The sum of the roots is 0 (m = 0) and the product is -1 (n = 1).

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

The sum of the roots is -p = 3 + 4 = 7, hence p = -7.

Using the sum of roots formula, p = -(3 + (-2)) = -1, hence p = -1.

The product of the roots gives p = 2 * 4 = 8.

The discriminant is 4² - 4*1*4 = 0, indicating one distinct root.

For real and distinct roots, the discriminant must be positive: 2² - 4*1*k > 0, which simplifies to k < 1.

The equation can be factored as (x + 2)² = 0, giving the double root x = -2.

Using the product of roots: k = 2 * (-6) = -12. The sum is 2 + (-6) = -4, which matches.

Using the product of roots: k = 4 * 4 = 16.

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

Factoring gives (x - 4)(x + 2) = 0, hence the roots are 4 and -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 discriminant is b² - 4ac = (-12)² - 4*4*9 = 144 - 144 = 0.

The discriminant is b² - 4ac = 6² - 4*1*9 = 0.

The discriminant D = 2² - 4*1*5 = 4 - 20 = -16, which indicates complex roots.