- #1
aheight
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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:
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?
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?