Final answer:
Without a specific polynomial equation provided, we cannot verify the stated roots and multiplicities. The multiplicity of a root indicates how many times it is repeated as a solution of the equation. In a quadratic equation, roots are found using the quadratic formula and the multiplicity relates to the power of the factor in the equation. The correct answer is option a) Root: 0, Multiplicity: 2.
Step-by-step explanation:
To determine the roots and their multiplicities for a polynomial equation, one would typically factor the equation or use the quadratic formula if it is a quadratic equation. However, the question that was asked does not provide a specific equation to work with but rather provides a set of roots and their supposed multiplicities.
Therefore, without the corresponding polynomial equation, it is impossible to verify if these roots and multiplicities are accurate. In general terms, the multiplicity of a root refers to the number of times that root is repeated as a solution of the equation.
When applying the quadratic formula, which is used for equations of the form ax² + bx + c = 0, the roots (solutions) can be found using the expression: -b ± √(b² - 4ac) over 2a. The signs and values of a, b, and c affect the solutions derived from this formula.
In polynomial equations, a root with a multiplicity greater than 1 indicates that the corresponding factor is raised to a power equal to the multiplicity. For example, a root of 0 with multiplicity 2 suggests a factor of the form (x-0)² or x² in the equation.