If α is a root of p(x) = 0, which statement is correct?

Correct answer: p(α) = 0

The governing definition of a root, or zero, of a polynomial is a value of the variable that makes the polynomial equal to zero. Thus, if α is a root of p(x) = 0, substituting x = α into the polynomial gives p(α) = 0. The value p(α) cannot generally be declared positive or negative; that depends on the particular polynomial and the selected value. Option D is also incorrect because it says the entire polynomial p(x) equals α, whereas the definition requires evaluating p at α. The statement p(α)=0 is universally valid for every root. Hence option B is the only correct answer.