Find the smallest positive integral value of k if the equation x 2 + 3x + k = 0 has roots with imaginary numbers. A missile is fired vertically into the air. The distance s (in m) above the ground as...

Find the smallest positive integral value of k if the equation x²
+ 3x + k = 0 has roots with imaginary numbers.

A missile is fired vertically into the air. The distance s (in m) above the ground as a function of time t (in s) is given by s = 100 + 500t - 4.9t². (a) When will the missile hit the ground? (b) When will the missile be 1000 m above the ground?