To determine the value of b in the second and third expressions, we can set them equal to zero and then solve for x.

For the second expression:

5x^2 + bx + 20 = 0

This is a quadratic equation that can be solved using the quadratic formula:

x = (-b ± √(b^2 - 4ac))/2a

where a = 5, b = b, and c = 20.

The discriminant (b^2 - 4ac) must be greater than or equal to zero for the equation to have real roots. So,

b^2 - 4ac ≥ 0
b^2 - 4(5)(20) ≥ 0
b^2 - 80 ≥ 0
b^2 ≥ 80
b ≥ √80
b ≥ 8.94 (approximately)

Therefore, b must be greater than or equal to 8.94.

For the third expression:

3x^2 + bx + 16 = 0

Similarly, we have:

b^2 - 4ac ≥ 0
b^2 - 4(3)(16) ≥ 0
b^2 - 192 ≥ 0
b^2 ≥ 192
b ≥ √192
b ≥ 13.85 (approximately)

Therefore, for the third expression, b must be greater than or equal to 13.85.