(3k – 100)(k + 35) < 0.
You want every (...) to have different sign so
the first () if k>33.333 ()>0 if k<33.333 ()<0 κ -35 33.333
the second () if k>-35 ()>0 if k<-35 ()<0 (1) - - +
(2) - + +
Finally + - +
You want (3k – 100)(k + 35) be <0 so -35
κ between -35 and 33.333