Part 1:
Find any and all quadratic functions
f(x)=x
2+bx+c with roots {b,c}.
Part 2:
Find any and all pairs of quadratic functions
f1(x)=x2+b1x+c1 with roots {b2,c2} and
f2(x)=x2+b2x+c2 with roots {b1,c1}.
Part 3:
Find any and all trios of quadratic functions
f1(x)=x2+b1x+c1 with roots {b2,c2},
f2(x)=x2+b2x+c2 with roots {b3,c3}, and
f3(x)=x2+b3x+c3 with roots {b1,c1}.
Assuming that my thoughts about Part 3 are accurate, here is a conjecture for Part N
For even N
----------------
(b1, b2,....., bN | c1, c2, ....., cN)
= (1,1,,.....,1| -2, -2, ......., -2) and (m, -m, .....,m, -m | 0. 0. ....., 0)
---------------
(b1, b2, ....., bN | c1, c2, ...., cN)
= (1,1,......,1| -2, -2, ......, -2) and, (0,0,....., 0 | 0, 0, ......, 0)
**** Mathematicians better versed than myself in analytical techniques and computer program experts may wish to comment on this.
Edited on June 16, 2022, 10:53 am
Conjecture about General N
