g(x) is a quadratic function given by:
g(x) = x² + 12x + 30.

Determine all possible real roots of this equation:
g(g(g(g(g(x))))) = 0

A graph of g(x) is a parabola with a minimum at (-6,-6)
A graph of g(x) - c is a parabola with a minimum at (-6,-6-c)
The interesting thing about this is g(x)-c  has two roots, one less than -6 and the other greater than -6.  But if c is less than -6 the roots are imaginary.
So if we work backwards we only need the + of the ħin the quadratic formula.
So here is what I did on my calculator:
0 [enter]
0
(-12+√(12²-4(30-[ans]))/2 [enter]
-3.550510257
-4.43491542
-4.748966595
-4.881503954
-4.942410266

Posted by Jer on 2013-11-04 15:43:48