Question 548737: I need to find all zeros
13x^3-185x^2+608x-580
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! I would first look for a rational zero and divide.
A rational zero would be a fraction whose numerator divides 580 and whose denominator divides 13.
The prime factorization of 580 is 
That means it has 12 positive divisors: 1,2,4,5,10,20,29,58,116,145,290, and 580.
Considering the possible denominators 1 and 13 (divisors of 13), that would make 24 positive rational numbers. With the corresponding 24 negative ones, that's 48 possible zeros to try.
Luckily, 2 is a zero of that polynomial. Dividing by 
I find 
Applying the quadratic formula to 
we can find any remaining zeros.
That gives us  and  as the last two zeros.
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