Question

x^3-6x^2+11x-6=0 iska mool nikale​

Answer 1

Answer:

Assume, for the generality of it, that we have the equation

anxn+…+a1x+a0=0  where all coefficients are integers.

Construct the two sets  A0  consisting of all divisors of  a0  (in this case  A0={1,2,3,6} ), and  A1  consisting of all divisors of  an  (in this case  A1={1} .  

If the equation has a rational solution  ±pq , then  p∈A0,q∈A1 .

Thus, in this case, the only possible rational solutions are 1/1, 2/1, 3/1, 6/1, -1/1, -2/1, -3/1, -6/1. Additionally, we can see that no solution may be negative (that would have given a sum of four negative terms, adding to zero), so we have only four numbers to try: 1,2,3, and 6.

Of course, besides trial and error, we have no way to guarantee that this will provide us with a solution, but we can then say that any solution - beyond what this trial run gave - will be irrational, and may require the general formula for the solution of a cubic equation (in this case)

Step-by-step explanation: