Zero of a Polynom and of a function

[Gil]

According to astronomical theory of planets VSOP2013,
the tropical year is given at an instant t by the following expression:

f=.2421904482-
.00006116623*t-
.000000065922*t^2+
2.667909E-7*t^3+
9.47396E-10*t^4+
1.06233E-10*t^5+
3.71993E-10*t^6,
with t= (Julian Day - 2451545)/365250.

I look for a possible minimum value of f, and therefore take the derivative of f and set it equal to 0:

fp=2.231958E-9*t^5+
5.31165E-10*t^4+
3.789584E-9*t^3+
8.003727E-7*t^2-
.000000131844*t-
.00006116623.

Two ways to get a solution on the HP50G:

a) with ROOT
'2.231958E-9*t^5+
5.31165E-10*t^4+
3.789584E-9*t^3+
8.003727E-7*t^2-
.000000131844*t-
.00006116623'

't' 6 ROOT
And get the correct output 6.51025795855 for t.

b) with the Solver for Polynoms (Right Shift Arrow followed by the key 7, and choose option 3)
Let's put the array [an... a0] in the order, as requested:
[ 2.231958E-9 5.31165E-10 3.789584E-9 8.003727E-7 .000000131844 -.00006116623 ]

and ask for the "solution".

Look for real solutions/output:
—> first element of the array is real : 6.45537286594 for t in this case.

Why this huge discrepancy in the real solution?

I thank you in advance for your answer.

Regards,
Gil Campart