By means of the Eisenstein criterion show that the cubic 4x3

By means of the Eisenstein criterion, show that the cubic 4x^3 - 3x - 1/2 is irreducible over Q

Solution

According to Eisenstein criterion,f(x) is irreducible over Q if there exist a prime no which divides all cofficient of polynomial expect highest power coff. Also, p2 does not divide costent term .

In this question , if multiply poly. By 2 then we can apply Eisentien criterion . But after multiplying by 2 , we can\'t find a prime no which divide 6 and 1 but doesn\'t divide 8.

Thus we cant show show from eisentein criterion that polynomial is irreducible over Q...