Question

A polynomial function p has three distinct zeros each with a multiplicity of one and its leading coefficient is positive. The polynomial function she has exactly one zero with a multiplicity of three and its leading coefficient is negative. The rational function age can be written as the quotient of p?

Answer 1

The rational function age can be written as [(x - a)(x - b)(x - c)] / {-(x - d)^3} where a, b, c are the zeros of the polynomial p with multiplicity of one and d is the zero of the polynomial q with multiplicity of three.

Step-by-step explanation:

A polynomial function with three distinct zeros, each with a multiplicity of one, and a positive leading coefficient can be written in the form p(x) = (x - a)(x - b)(x - c), where a, b, and c are the zeros. A polynomial function with one zero of multiplicity three and a negative leading coefficient can be written in the form q(x) = -(x - d)^3, where d is the zero. To express the rational function age(x) = p(x) / q(x) as the quotient of these two polynomial functions, we replace p(x) and q(x) with their respective forms, resulting in age(x) = [(x - a)(x - b)(x - c)] / {-(x - d)^3}.