Question 1020839
By the rational root theorem, the rational root is of the form


*[tex \large x = \pm \frac{p}{q}]


where p and q are positive integers and p is a factor of 5, q is a factor of 3. Moreover, the root must be negative (since all coefficients are positive, so it can't possibly have a positive root). So you only need to check -1/1, -1/3, -5/1, and -5/3.


Once you have found the rational root x_0, divide by (x - x_0) to obtain a 3rd degree polynomial. The 3rd degree polynomial must have a rational root; if it is rational, then you can use the rational root theorem again, otherwise you might need to use a calculator. Once you have found the second root, divide again to obtain a quadratic polynomial, in which you can solve using the quadratic formula.