Final answer:
The polynomial p(x) of degree 3 with a root of multiplicity 2 would have a factor of (x-a)², where a is the repeated root, and could potentially be solved for other roots using the quadratic formula if set equal to zero.
Step-by-step explanation:
The question refers to a polynomial of degree 3, p(x), with a specific interest in a root of multiplicity 2. In the context of polynomials, a root of multiplicity 2 means that the root occurs twice, indicating that the factor corresponding to that root is squared in the polynomial's factored form. For example, if the root is x=a, then (x-a)² would be a factor of p(x).
When dealing with third-degree polynomials, if we have a root of multiplicity 2, say at x = r, then the polynomial can be expressed in the form p(x) = (x-r)²(x-s), where s is another root of the polynomial. The Solution of Quadratic Equations might be used if we set p(x) equal to zero and find the roots, applying the quadratic formula to the squared term.