[R] How to find the zero (only the real solution) with the package polynom ?

[Ptit_Bleu]

Hello,

I have 3 columns : a, b and a*b
I would like to find the pair (a,b) so that a*b is the minimum but not from
the points I measured but from the fit of the curve (I have more points that
the ones given below but I fit only on this part because I 
know that the minimum a*b is in this interval).

I thought doing it this way :

- to fit a*b=f(a)
abfit<-lm(ab ~ poly(a,8,raw=T))

- to use the package polynom to make the polynom 
library(polynom)
polynomial(abfit$coefficients)
0.03537506 - 0.8506516*x + 8.302545*x^2 - 44.80418*x^3 + 144.2161*x^4 -
283.2458*x^5 + 331.1776*x^6 - 210.5144*x^7 + 55.86646*x^8

- to derive the polynom
deriv(polynomial(pfit$coefficients))
-0.8506516 + 16.60509*x - 134.4125*x^2 + 576.8643*x^3 - 1416.229*x^4 +
1987.066*x^5 - 1473.601*x^6 + 446.9317*x^7

- to find the zero
solve(deriv(polynomial(pfit$coefficients)))
[1] 0.1749897+0.0568886i 0.1749897-0.0568886i 0.3742571-0.1235393i
0.3742571+0.1235393i 0.4778418+0.0000000i 0.8604070+0.1306799i
0.8604070-0.1306799i

And here is my little problem : I don't want the complex solutions, only the
real one (0.4778418).

I also tried uniroot but I got an error message :
uniroot(deriv(polynomial(pfit$coefficients)), c(0.8,0.2))
Error in uniroot(deriv(polynomial(abfit$coefficients)), c(0.8, 0.2)) : 
        Impossible to find the function "f"

Is there a way to extract this real solution ?

I thank you in advance for your help,
Have a nice day,
Ptit Bleu. 

-------------------------------------------------
Set of points
a        b                    a*b
0.8	0.033320357	0.026656286
0.76	0.023930636	0.018187283
0.72	0.0153903	0.011081016
0.68	0.007844914	0.005334542
0.64	0.001598132	0.001022804
0.6	-0.00315939	-0.001895634
0.56	-0.006402796	-0.003585566
0.52	-0.008379886	-0.004357541
0.48	-0.009528793	-0.004573821
0.44	-0.010198446	-0.004487316
0.4	-0.010638282	-0.004255313
0.36	-0.010937536	-0.003937513
0.32	-0.011169004	-0.003574081
0.28	-0.011343229	-0.003176104
0.24	-0.0114878	-0.002757072
0.2	-0.011630636	-0.002326127
0.16	-0.011724586	-0.001875934

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