The discriminant must be non-negative: 2^2 - 4*1*k >= 0, thus k <= 1.

The discriminant must be non-negative: 2^2 - 4*1*k >= 0 leads to k <= 1.

The discriminant is 0 (b^2 - 4ac = 16 - 16 = 0), indicating real and equal roots.

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

The discriminant must be negative: 4^2 - 4*1*k < 0 => 16 < 4k => k > 4.

The discriminant must be non-negative: 4^2 - 4*1*k >= 0, which simplifies to k <= 4.

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

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

The discriminant D = 6^2 - 4*1*9 = 0, indicating real and equal roots.

The discriminant must be positive: 6^2 - 4*1*k > 0, which simplifies to k < 9.

The discriminant must be non-negative: 6^2 - 4(1)(k) ≥ 0, which gives k ≤ 9.

The product of the roots is n = 2 * 3 = 6.

The sum of the roots is -(-2) + -(-3) = 5, hence p = 5.

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

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

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

Setting the discriminant to zero: (-6)^2 - 4*1*k = 0 gives k = 9.

If one root is 3, then substituting x = 3 gives 3^2 - 6*3 + k = 0, leading to k = 9.

The roots can be found by factorization: (x - 3)(x - 5) = 0, hence the roots are 3 and 5.

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.

For l=1, m_l can take values -1, 0, 1, which gives 3 possible values.

At equilibrium, [A] = 0.5 - 0.2 = 0.3 M.

At equilibrium, 0.5 - 0.2 = 0.3 M of A remains.

Increasing the concentration of a product shifts the equilibrium to the left to counteract the change.

Using ICE table and Kc expression, we find [NO2] at equilibrium to be 0.2 M.

The equilibrium constant Kc is only affected by temperature, not by changes in concentration.

Decreasing the volume increases the pressure, and the equilibrium will shift towards the side with fewer moles of gas, which is the right side (2 moles of SO3).

Decreasing the volume increases the pressure, and according to Le Chatelier's principle, the equilibrium will shift towards the side with fewer moles of gas, which is the right side in this case.