Final answer:
A polynomial function with three distinct zeros, each with multiplicity 1, and a positive leading coefficient can be written as p(x) = a(x - r)(x - s)(x - t). The values of (p'₁ + p'2) and (p₁ + P₂) will be equal.
Step-by-step explanation:
A polynomial function with three distinct zeros, each with multiplicity 1, and a positive leading coefficient, can be written as:
p(x) = a(x - r)(x - s)(x - t)
where r, s, and t are the zeros of the polynomial and a is the leading coefficient. Since the zeros have multiplicity 1, they are distinct. The values of (p'₁ + p'2) and (p₁ + P₂) will have the same value because the derivative of a polynomial only affects the coefficients, not the zeros themselves. So, option b is correct: the values of (p₁ + P₂) and (p'₁ + p'₂) are equal.