Can someone help me distinguish when Solve[polynomial==0,x] returns exact solutions as opposed to solutions in terms of Roots? For example, if I code:(adsbygoogle = window.adsbygoogle || []).push({});

myroots = x /. Solve[1/2 + 1/5 x + 9/10 x^2 + 2/3 x^3 - 1/5 x^4 + 3/11 x^5 == 0, x]

this cannot be solved in terms of radicals so Solve returns Root objects:

{Root[165+66 #1+297 #1^2+220 #1^3-66 #1^4+90 #1^5&,1],

Root[165+66 #1+297 #1^2+220 #1^3-66 #1^4+90 #1^5&,2],

Root[165+66 #1+297 #1^2+220 #1^3-66 #1^4+90 #1^5&,3],

Root[165+66 #1+297 #1^2+220 #1^3-66 #1^4+90 #1^5&,4],

Root[165+66 #1+297 #1^2+220 #1^3-66 #1^4+90 #1^5&,5]}

but

myroots = x /. Solve[1/2 + 1/5 x + 9/10 x^2 + 2/3 x^3 - 1/5 x^4 == 0, x]

returns exact solutions in terms of radicals. I can't figure out how to distinguish the two as in:

If[solve returns exact solutions,

do this;

,

else if Roots are returned do this

]

Can someone help me do this?

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# Mathematica How to distinguish exact roots using Solve?

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