The standard value of gravitational acceleration at the surface of the Earth is approximately 9.81 m/s^2.

The standard value of gravitational acceleration on the surface of the Earth is approximately 9.8 m/s².

i^4 = (i^2)^2 = (-1)^2 = 1.

The discriminant must be non-negative: (2k)^2 - 4(1)(16) ≥ 0. This gives 4k^2 - 64 ≥ 0, leading to k^2 ≥ 16, so k ≥ 4.

For equal roots, the discriminant must be zero: k^2 - 4*1*16 = 0, thus k^2 = 64, giving k = -8 or 8. The answer is -4.

The discriminant must be less than zero. Thus, k^2 - 4*1*16 < 0 leads to k^2 < 64, giving k < 8 and k > -8.

The discriminant must be negative: k^2 - 4*1*9 < 0 => k^2 < 36 => |k| < 6, hence k > 6.

If the roots are reciprocals, then k = sum of roots = 0 and product = 1. Thus, k = 2.

For equal roots, the discriminant must be zero: (-4)^2 - 4*1*k = 0 => 16 - 4k = 0 => k = 4.

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

Setting 2k + 2 = 0 gives k = 2.

Setting k(0) = 0^2 + 1 gives k = 1.

Setting k(2) = 2^2 gives 2k = 4, thus k = 2.

The minimum value occurs at x = -b/(2a) = -2/(2k). Setting f(-1) = -3 gives k = -2.

For no real roots, the discriminant must be less than zero: k^2 - 4*1*16 < 0 => k^2 < 64 => |k| < 8.

For the roots to be equal, the discriminant must be zero. Thus, k^2 - 4*1*16 = 0, which gives k^2 = 64, so k = ±8.

For equal roots, the discriminant must be zero. Thus, k^2 - 4*1*4 = 0, which gives k^2 = 16, so k = ±4.

For both roots to be negative, k must be negative and greater than the square root of the discriminant. Thus, k < -6.

The sum of the roots is 3 + 3 = 6, so k = 6.

The sum of the roots is 3 + 3 = 6, so k = 6.

For both roots to be positive, k must be greater than 6 (sum of roots) and k^2 - 36 > 0 (discriminant). Thus, k > 6 and k < 12.

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

For no real roots, the discriminant must be less than zero: (-4)² - 4*1*k < 0, hence k > 4.

Since the roots are equal, k = 4 + 4 = 8.

For equal roots, the discriminant must be zero: k^2 - 4*1*16 = 0, thus k^2 = 64, giving k = -8 or k = 8. The answer is -8.

The discriminant must be less than zero: k^2 - 4*1*16 < 0 => k^2 < 64 => k < 8 and k > -8.

For real and distinct roots, the discriminant must be positive: k^2 - 4(1)(16) > 0. Thus, k^2 > 64, leading to k < -8 or k > 8.

For both roots to be negative, k must be negative and |k| > 8. Thus, k = -8.

For real and distinct roots, the discriminant must be positive: k^2 - 4(1)(16) > 0. Thus, k^2 > 64, leading to k < -8 or k > 8.

For one real root, the discriminant must be zero: k^2 - 4*1*25 = 0, thus k^2 = 100, giving k = -10 or k = 10.