Teaching Haryana (HPSC) Assistant Professor Mock Test 2025 Mathematical Science Algebra Polynomial Rings and Irreducibility Criteria
Consider the polynomial f(x) = x3 - 2 over Q, the field of rational numbers. Which of the following statements about f(x) is NOT correct?
1
f(x) is reducible over Q because there exists a rational root.
2
f(x) is irreducible over Q by the Eisenstein's Criterion with p = 2.
3
f(x) is irreducible over Q because it has degree 3 and thus has no rational roots.
4
None of these
5
Question Not Attempted