MATLAB: Find roots from determinants

MATLABroots

I want to solve the equation by finding its roots with symbolically.
But why I get answer like this?
anyone can help?
syms a b c d e f A B C X Y Z N
eq1=C*e*f - B*N^2 - 2*C*N^2 - C^2*N - N^3 - 2*B*C*N - B*C^2 + N*e*f + N^2*X*a - N^2*Y*a + B*C*X*a - B*C*Y*a + B*N*X*a - B*N*Y*a + C*N*X*a - C*N*Y*a + Y*a*e*f
solve(eq1,N)
The aswers I get is
ans =
root(z^3 + z^2*(B + 2*C – X*a + Y*a) + z*(- e*f + C^2 + 2*B*C – B*X*a + B*Y*a – C*X*a + C*Y*a) – Y*a*e*f – B*C*X*a + B*C*Y*a – C*e*f + B*C^2, z, 1)
root(z^3 + z^2*(B + 2*C – X*a + Y*a) + z*(- e*f + C^2 + 2*B*C – B*X*a + B*Y*a – C*X*a + C*Y*a) – Y*a*e*f – B*C*X*a + B*C*Y*a – C*e*f + B*C^2, z, 2)
root(z^3 + z^2*(B + 2*C – X*a + Y*a) + z*(- e*f + C^2 + 2*B*C – B*X*a + B*Y*a – C*X*a + C*Y*a) – Y*a*e*f – B*C*X*a + B*C*Y*a – C*e*f + B*C^2, z, 3)

Best Answer

 solve(eq1,N,'maxdegree',3)
will give you the three roots in explicit formula form.
Howerver, unless you are much better mathematician than I am, the explicit formula will be very difficult for you to make sense out of. If you were working with degree 4, the explicit formula is, I would say, impossible to make any sense out of.
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