• @goku denominator is always positive as discriminant is less than 0 and coefficient of $x^2$ is positive. So to make the entire term negative the numerator shud be negative. So $2a-1$<$0$ and discriminant of numerator also less than 0. Solve these two conditions and u will get the answer.

• @goku denominator is always positive as discriminant is less than 0 and coefficient of $x^2$ is positive. So to make the entire term negative the numerator shud be negative. So $2a-1$<$0$ and discriminant of numerator also less than 0. Solve these two conditions and u will get the answer.

thank you very much for your help but I did not understand why D<0 and why 2a+1 is less than 0. CAN YOU PLEASE EXPLAIN ME THESE

• First D>0 means that the graph will be totally below the x axis or above the x axis. It will not cut nor touch the x axis.
Second, the sign of a, ie a>0 or a<0 will decide if graph opens above the x axis or below the x axis respectively.
So according to your question, 2a-1<0 and D>0.