axsquare + bx +c =y
u shaped , parabola
the shape when cuts the x-axis , the cut points are roots
roots are when Y=0
roots are what input makes output zero
there could be one root , two roots or no roots
i.e there could be only one value of input which makes output zero, two values of input which make output zero , or no values of input ever giving output zero.
we study roots since it gives us a snapshot of information which is enough to generate the bigger picture
roots are where y= 0 for some value of x
the shape could be cutting the x axis at one place (one root) , two places ( two roots) , or no places (zero roots )
imagine the shape see the shape
x axis is the input line , y axis is the output line
determinant is a easy way to check without actually making the equation on the graph or some such
determinant is = sqaure root of bsquare-ac
if determinant zero then one root one touch point for shape to touch cut x axis
if determinant more than zero then two roots , two touch points for the graph with the x axis
if determinant less than zero then no roots , no cutting the x axis
why how ?