Question

Select all the roots of the polynomial function.

a) -2
b) -1
c) 0
d) 1
e) 2

Answer 1

To determine the roots of a polynomial function, the quadratic formula is used with the coefficients provided. Several sets of coefficients are presented, but without knowing the exact polynomial these relate to, we cannot identify which roots are correct from the given options.

Step-by-step explanation:

To select all the roots of a polynomial function, particularly a quadratic one given by the equation ax²+bx+c = 0, we use the quadratic formula:

-b ± √(b² - 4ac) over 2a.

In this case, you've provided several different values for a, b, and c in separate versions of polynomial equations. Each set of coefficients corresponds to different quadratic equations and their respective roots can be found by substituting into the quadratic formula.

For example, if a = 1, b = 0.0211, and c = -0.0211, we would substitute these into the formula:

-0.0211 ± √(0.0211)² - 4(1)(-0.0211) over 2(1), which simplifies and gives us the potential roots.

However, without the specific polynomial function associated with the roots given as options (a) through (e), it is not possible to determine which of these roots, if any, are correct for the unknown function. To provide an accurate answer, the actual polynomial equation is necessary.