Consider the polynomial f(x) = x2025 - 1 over the finite field 𝔽5 with five elements. Let S be the set of all roots of f in an algebraic closure of 𝔽5. Which of the following statements is true?

If p(x) is a polynomial of degree n, consider the statements: P: If p(x) ∈ ℚ[x], then p(x) has n roots in ℚ. Q: If p(x) ∈ ℝ[x], then p(x) has n roots in ℝ. R: If p(x) ∈ &complex;[x], then p(x) has n roots in &complex;. Which of the following is true?

Let p > 2 be a prime number. Let &Double_struck;Fp denote the finite field with p elements and ‾&Double_struck;Fp be its algebraic closure. Which of the following statements is FALSE?