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Part BCSIR NET June 2023

Polynomial rings and irreducibility tests

How many real roots does the polynomial x3+3x−2023x^{3} + 3x - 2023 have?

  1. A.0
  2. B.1✓ Correct
  3. C.2
  4. D.3

You have the answer. Trap Analysis is why the other three were written.

Not a worked solution repeated four times — the specific reasoning error each wrong option was built to reward.

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50 are analysed free — try those first.

Related counterexample: Irreducible over ℤ ⇒ irreducible mod every prime

More on this topic

The chapter behind this: Irreducibility tests — free to read

From Rings and Fields › Polynomial rings and irreducibility tests

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