z^3 + 7z^2 + 10z > 0
z(z^2 + 7z + 10) > 0
z(z + 2)(z + 5) > 0
Solution set is given by,
all 3 terms +ve
1 term +v e and 2 terms -ve
This can be modelled as
+ + + > 0 --> z > 0 (z + 2) > 0 (z + 5) > 0 -> z > 0
+ - - > 0 --> z > 0 (z + 2) < 0 (z + 5) < 0 -> no solution
- + - > 0 --> z < 0 (z + 2) > 0 (z + 5) < 0 -> no solution
- - + > 0 --> z < 0 (z + 2) < 0 (z + 5) > 0 -> -5 < z < -2
There are thus two solution sets: z > 0 and -5 < z < -2