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The discriminant of
. 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
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
. Graphically, the curve will have no points of intersection with the x-axis.