Different answers from 'roots' & 'solve' command?

>> R=roots([3 0 0 0 0 4 1])

R =

     0.9017 + 0.6256i
     0.9017 - 0.6256i
    -0.2767 + 1.0147i
    -0.2767 - 1.0147i
    -1.0000 + 0.0000i
    -0.2502 + 0.0000i

>> R(R == real(R))

ans =

     -1.0000
     -0.2502

>> solx = solve(3*x^6 + 4*x + 1==0, x)

solx =

                                              -1
   RootOf(z^5 - z^4 + z^3 - z^2 + z + 1/3, z)[1]
   RootOf(z^5 - z^4 + z^3 - z^2 + z + 1/3, z)[2]
   RootOf(z^5 - z^4 + z^3 - z^2 + z + 1/3, z)[3]
   RootOf(z^5 - z^4 + z^3 - z^2 + z + 1/3, z)[4]
   RootOf(z^5 - z^4 + z^3 - z^2 + z + 1/3, z)[5]

>> solx(solx == real(solx))

ans =

-1

>>

[Subham Shit]

Using 'roots' I am getting 2 real solution but using 'solve' I am getting 1 real solution of same equation. How is that possible?

Answer 1

[Matt J]

SOLVE was not able to find a closed symbolic form for all the roots (because one doesn't exist for this polynomial). It therefore cannot assess whether the ones not in closed form are real.