Question 701633
Assuming you meant to type: x^3+4x^2+7x+28 = 0 



Possible Roots: List all the factors of 28


Possible Roots: 1, 2, 4, 7, 14, 28, -1, -2, -4, -7, -14, -28


Note: make sure you list the negative factors as well


Another Note: This trick only works if the leading coefficient is 1 or -1.

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Actual Roots: 


x^3+4x^2+7x+28=0 


(x^3+4x^2)+(7x+28)=0 


x^2(x+4)+7(x+4)=0


(x^2+7)(x+4) = 0


x^2+7 = 0 or x+4 = 0


x^2 = -7 or x = -4


x = sqrt(-7), x = -sqrt(-7), or x = -4


x = i*sqrt(7), x = -i*sqrt(7), or x = -4


The actual roots are x = i*sqrt(7), x = -i*sqrt(7), or x = -4


The first two are complex or imaginary roots. The third root is real and rational.


The only actual rational root is x = -4