Raymond B. answered • 11/11/22
Math, microeconomics or criminal justice
There are as many roots, solutions or zeros as the degree of the polynomial
for quadratic equations, there are always 2 solutions, although it could be "one" solution that repeats, multiplicity 2, or the 2 solutions may be imaginary. the imaginary solutions are conjugate pairs and do not repeat. The real solutions are either 0, "1," or 2. If 0 real solutions, then there are two imaginary solutions. If one real solution, it repeats, so there's techncially still two solutions, but they are the same. When there is "one" solution, it means the graph of the quadratic just touches the x axis, not crossing it, but tangent to it. That point of tangency is the parabola's vertex, with y coordinate =0. when there are 2 real and different solutions, the graph intersects the x axis twice. Where there are 0 real solutions the graph never touches or intersects the x axis. The discriminant of the quadratic, b^2-4ac tells you whether there are 0, 1 or 2 real solutions. if b^2-4ac>0, there are 2 real solutions. If b^2-4ac<0 there are 2 imaginary solutions. If b^2-4ac=0, there is 1 real solution.
