Hello from MrBillDoesMath!
Answer:
3, -2, 1 +\- sqrt(2)
Discussion:
By the "rational root theorem" the roots of the given polynomial are factors of the constant term 6. These factors are +\-1, +\-2, +\-3, or +\-6). Trial and error showed that -2 and 3 were root so
x^4-3x^3-5x^2+13x+6 =
(x-3)(x+2) (x^2 -2x - 1)
Next we solve for the roots of the quadratic using the quadratic equation.
Regards,
MrB
P.S. I'll be on vacation from Friday, Dec 22 to Jan 2, 2019. Have a Great New Year!