+128406 5x^2+19x+16 > 20 subtract 20 from both sides
5x^2 + 19x - 4 > 0 factor
(5x - 1) ( x + 4) > 0
Setting both factors to 0,.....we can establish 3 possible intervals
5x - 1 = 0 x + 4 = 0
5x = 1 x = -4
x = 1/5
The possible intervals that provide solutions are
(-inf, - 4) U ( - 4, 1/5) U ( 1/5, inf )
And either the middle interval solves the original inequality or the two outside intervals do
Testing a point in the middle interval - I'll pick 0 - in the original inequality we have
5(0)^2 + 19(0) + 16 > 20 is false
So...since we are looking for the integer that make the inequality false....the solution will be all the integers on ( - 4, 1/5)
And the integers in this interval are -3, -2, -1, 0
So.... 4 integers do not satisfy this
