Final answer:
To find the zeros of a quadratic equation, the quadratic formula is used. Zeros are the x-values where the graph intersects the x-axis, and they must be verified to ensure they're not extraneous solutions. Answers in the form of points such as (0,0) and (7,0) show these x-values as points on the graph.
Step-by-step explanation:
To find the zeros of the quadratic equation x² + 0.0211x - 0.0211 = 0, we use the quadratic formula, which is x = ∛(-b ± √(b² - 4ac))/(2a) where a, b, and c are coefficients from the equation ax²+bx+c = 0. In this case, a=1, b=0.0211, and c=-0.0211. Plugging these values into the quadratic formula, we find the potential zeros.
It is important to note that when solving quadratic equations, we may sometimes obtain extraneous solutions, which are solutions that do not satisfy the original equation. So, after finding the potential zeros, they must be validated by substituting them back into the original equation.
The answer choices provided seem to be referencing points on a graph rather than just the x-values of the zeros. Zeros of a function are the x-values where the function crosses the x-axis, and they are represented as points (x,0). Extraneous solutions are those that, when plugged back into the equation, do not hold true.
Option B suggests the correct method of presenting zeros, which are (0,0) and (7,0) if 0 and 7 are the solved zeros of the equation; however, these need to be calculated accurately using the quadratic formula and verified.