The discriminant is 2^2 - 4*1*1 = 0, indicating that the roots are real and equal.

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

The equation can be factored as (x + 1)^2 = 0, giving the root x = -1.

Substituting x = -1 into the equation gives (-1)^2 + 2(-1) + k = 0, leading to 1 - 2 + k = 0, thus k = 1.

The product of the roots is 1 * (-3) = -3, hence k = -3.

For both roots to be negative, k must be greater than 0.

For both roots to be negative, k must be greater than 0.

For both roots to be positive, k must be less than 4 (from the condition of the sum and product of roots).

The discriminant is 0, indicating one real root (a repeated root).

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

Substituting x = 2 into the equation gives 2^2 + 5(2) + k = 0, leading to 4 + 10 + k = 0, thus k = -14.

The discriminant is 0, indicating one real root (a repeated root).

For both roots to be positive, k must be greater than 9 (since the sum of roots is -b/a and must be positive).

For both roots to be positive, k must be greater than 12 (from Vieta's formulas). The minimum integer k is 13.

The discriminant must be positive: k^2 - 4*1*16 > 0, which simplifies to k^2 > 64, hence k < -8 or k > 8.

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

Using Vieta's formulas, p = -(3 + (-2)) = -1 and q = 3 * (-2) = -6. Therefore, p + q = -1 - 6 = -7.

Using Vieta's formulas, p = -(3 + 4) = -7 and q = 3 * 4 = 12. Therefore, p + q = -7 + 12 = 5.

The equation can be factored as (x - 5)^2 = 0, giving the root x = 5.

Factoring gives (x - 3)(x - 5) = 0, hence the roots are 3 and 5.

Circumference = 2πr = 2π × 7 cm = 14π cm.

Circumference = 2πr = 2 × 3.14 × 7 cm = 43.96 cm.

Circumference = 2 * π * radius = 2 * π * 7 = 14π units.

The area of a circle is given by A = πr². If the radius is doubled (r becomes 2r), the new area is A' = π(2r)² = 4πr², which is four times the original area.

Volume = (4/3) * π * (radius)³ = (4/3) * π * (3)³ = (4/3) * π * 27 = 36π cm³

Total members in Rajya Sabha = 245. Nominated members = 12. Therefore, elected members = 245 - 12 = 233.

Percentage of nominated members = (12/245) * 100 = 4.89%.

Percentage of nominated members = (12 / 245) * 100 = 4.89%.

Percentage of nominated members = (12/245) * 100 = 4.89%.

Elected members = Total members - Nominated members = 245 - 12 = 233.