The number of irrational roots of $(x^2 -3x +1)(x^2 +3x +2)(x^2 -9x + 20) = -30$ is___? 

The number of irrational roots of $(x^2 -3x +1)(x^2 +3x +2)(x^2 -9x + 20) = -30$ is___?



My Approach : 
Multiplying the above equation and then apply Descartis rule is very lengthy method. Also I tried it by taking factors of $30$ and then solving the equation but that is also going very lengthy . 
Please suggest some good method of doing this.

Note that the polynomial is a sixth degree monic polynomial whose constant term is $70$. Hence, by rational roots theorem, the possible roots can only be divisors of $70$. You will find that none of the roots are rational.
