What is the significance of

TLDR: The material of elementary algebra is full of interesting results and challenging problems, but elementary algebra seemed different. as mentioned in this paper continue to be astonished at how the material of school mathematics provides scope for investigations of considerable depth.

Abstract: I continue to be astonished at how the material of school mathematics provides scope for investigations of considerable depth. Elementary geometry and number theory are full of interesting results and challenging problems, but elementary algebra seemed different. I thought that I knew a bit about the real quadratic function f (x) = ax − bx + c. (My choice of a negative sign for the second term is deliberate.) Certainly I knew that when there was something special about . I knew too that and give rise to different situations. However, it never occurred to me that , and had anything special about them, let alone and a host of other particular values. b = 4ac f (x) b > 4ac b < 4ac b = ac b = 2ac b = 3ac b = 2 (3 + 5) ac