Log in Start free

Part BCSIR NET June 2023

Polynomial rings and irreducibility tests

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

A.0
B.1✓
C.2
D.3

Solution

The derivative $3 x^{2} + 3 > 0$ , so the cubic is strictly increasing: exactly one real root.

Related counterexample: Irreducible over ℤ ⇒ irreducible mod every prime

More on this topic

irreducible over Q not mod pDecember 2023

From Rings and Fields › Polynomial rings and irreducibility tests

ShareWhatsApp Telegram