Question 135205
The discriminant of {{{ax^2+bx+c=0}}} is {{{ b^2-4*a*c }}}.  For your equation, a = 1, b = 2, and c =1.


If the discriminant is >0 (positive), then there are two different real roots to the equation.  Graphically this means that the graph of the function {{{y=ax^2+bx+c}}} will intersect the x axis in two different points.


If the discriminant = 0, then there are two real and identical roots (or one real root with a multiplicity of two).  Graphically, this means that the curve is tangent to the x-axis at the vertex of the parabola and there is one point of intersection, or one x-intercept.


If the discriminant <0, (negative), then there are no real roots, although there is a conjugate pair of complex roots involving the imaginary number i where i is defined as {{{i^2=-1}}}.  Graphically, the curve will have no points of intersection with the x-axis.