Let P = {p : ℝ → ℝ | p is a polynomial} be the vector space formed by polynomials. Which of the following statements is true?
a) If p(x) = aₙxⁿ + ... + a₁x + a₀ = 0 for all x in ℝ, then aⱼ = 0 for all j in {0, ..., n}.
b) If p(x) = aₙxⁿ + ... + a₁x + a₀ ≠ 0 for all x in ℝ, then aⱼ ≠ 0 for all j in {0, ..., n}.
c) If p(x) = aₙxⁿ + ... + a₁x + a₀ = 0 for some x in ℝ, then aⱼ = 0 for some j in {0, ..., n}.
d) If p(x) = aₙxⁿ + ... + a₁x + a₀ ≠ 0 for some x in ℝ, then aⱼ ≠ 0 for some j in {0, ..., n}.