Given an equation ax^2+bx+c=0
what values a,b cause the roots of the equation to be a and b and the discriminant to be equal to c?
Well yes, if the roots are a and b, then (x-a)(x-b) = 0
Multiplying by a gives
ax2 -a(a+b)x +a2b = 0
Comparing the two equations, gives
(1) b = -a(a+b) which leads to b = -a2/(a+1), just as Dej Mar says
Also,
(2) c = a2b
and
(3) c = the discriminant = b2 -4ac
Solving (1), (2), and (3) should lead to discrete a, b and c values which constitute the solution
Three equations
