but its asking for the range of values for a not for the number of roots?
You sub the equations together and rearrange which gives you a general equation where a varies.For the graphs to have two points of intersection the general equation found needs to have two roots,thus you use discriminant
You sub the equations together and rearrange which gives you a general equation where a varies.For the graphs to have two points of intersection the general equation found needs to have two roots,thus you use discriminant
Consider an easier example if you are confused. Consider the curve y=x2+a and the line y=0 which is of course just the x-axis. You should be able to see that if a>0 then the curve lies completely above the x-axis so there are no points where the graphs intersect. If a=0 then there is a single (repeated) root. If a<0 then there are two distinct points of intersection. So if someone told you that the curve y=x2+a crosses the x-axis at two distinct points then you’d have to have a<0. This is the same as your example, it’s just a bit more complicated.
Consider an easier example if you are confused. Consider the curve y=x2+a and the line y=0 which is of course just the x-axis. You should be able to see that if a>0 then the curve lies completely above the x-axis so there are no points where the graphs intersect. If a=0 then there is a single (repeated) root. If a<0 then there are two distinct points of intersection. So if someone told you that the curve y=x2+a crosses the x-axis at two distinct points then you’d have to have a<0. This is the same as your example, it’s just a bit more complicated.