Final answer:
To find the zeros of a polynomial function, set the function equal to 0 and solve for x, often using factoring or the quadratic formula for quadratic equations.
Step-by-step explanation:
To find the zeros of a polynomial function, you should set the function f(x) equal to 0 and solve for the variable. This process often involves factoring the polynomial, if possible, or using the quadratic formula if the polynomial is of the second degree (quadratic). For instance, given a quadratic equation in the form ax² + bx + c = 0, you can use the quadratic formula which is x = (-b ± √(b²-4ac)) / (2a). Let's consider an example equation, x² + 0.0211x - 0.0211 = 0:
- Identify the coefficients, which are a = 1, b = 0.0211, and c = -0.0211.
- Plug these values into the quadratic formula.
- Calculate the discriminant, which is b² - 4ac.
- Use the values for b, b² - 4ac, and a to find the two possible values for x that make the equation zero.
This will give you the x-values where the polynomial equals zero, that is, its zero points on the graph, also known as roots or solutions of the equation.