Originally Posted by

**godelproof** Consider a simple one like this:

2(x+1)(2x-1)=x(x-1)(x+2)

the "solve" command gives:

x1=1/3*(54+3*i*705^(1/2))^(1/3)+7/(54+3*i*705^(1/2))^(1/3)+1

x2=-1/6*(54+3*i*705^(1/2))^(1/3)-7/2/(54+3*i*705^(1/2))^(1/3)+1+1/2*i*3^(1/2)*(1/3*(54+3*i*705^(1/2))^(1/3)-7/(54+3*i*705^(1/2))^(1/3))

x3=-1/6*(54+3*i*705^(1/2))^(1/3)-7/2/(54+3*i*705^(1/2))^(1/3)+1-1/2*i*3^(1/2)*(1/3*(54+3*i*705^(1/2))^(1/3)-7/(54+3*i*705^(1/2))^(1/3))

But we know that all 3 roots of the equation are REAL NUMBERS. So this result is not so satisfying to me... My question is this: how can we know if one solution is intrinsically complex or real, when it gives us results like these?

(btw, I remember there's a command that numerically finds zero of a polynomial, what's its name, please?)