Quadratic Solver for Casio FX-3650P

[Albert Chan]

(07-18-2018 04:35 PM)Albert Chan Wrote:  Borrowing Klemm example, solve F(z) = 11713 z^2 - 1470492 z + 46152709 = 0

Just by looking at the coefficients, my Casio cannot give exact B^2 - 4AC
So, try reduction with offset X ~ -B/(2A) = 62.77179203 ...

With a little bit of work, above discriminant can be calculated exactly
Say, a calculator only have 10 digits precision, so any 5-digits multiply are exact:

B^2 = 1470492^2
= (14e5 + 70492)^2
= (14e5 + 2*70492) * 14e5 + 4969122064
= (21573776 + 49691) * 1e5 + 22064
= 21623467e5 + 22064

4 A C = 4 * 11713 * 46152709
= 46852 * (461e5 + 52709)
= 21598772e5 + 2469522068
= 21623467e5 + 22068

D = B^2 - 4 A C = 22064 - 22068 = -4

I shown the steps, but on the calculator, it is much simpler:
B^2 - 4AC = (14e5 + 70492)^2 - 46852 * (461e5 + 52709)

1e5 terms:
(14e5 + 2*70492)*14e5 - 46852*461e5 => -24996e5

D = (reduced B^2 - 4AC) + (1e5 terms):
70492^2 - 46852*52709 + Ans => -4