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> > The number of irrational roots of $(x^2 -3x +1)(x^2 +3x +2)(x^2 -9x + 20) = -30$ is\_\_\_?
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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.