Q8: a,b,c,d + – ve

Picture

This We come back to the Graphical Avatars of the Quadratic function approaching from the algebra to the geometry.

So, we have taken
a, b, c & D and have considered all the possibilities of their signs, drawn a small graph for each. This is the first part with 8 cases for a>0 and we have another 8 cases below for a<0 i.e. inverted U graphs. 

Do you see that 2 out of the 8 cases HAVE NO ROOTS
and strangely 2 out of these 8 cases are NOT POSSIBLE


These are the cases when a<0 in the quadratic function leading to an inverted graph. 

As in the previous 8 cases, in these too there are TWO CASES WHICH ARE NOT POSSIBLE

AND 
TWO MORE CASES WHERE THERE ARE NO ROOTS.