Final answer:
A polynomial function with zeros calculator aids in determining and factoring the zeros of a polynomial, finding the sum and product of the roots, and graphing polynomial equations using techniques such as the quadratic formula and root calculations.
Step-by-step explanation:
A polynomial function with zeros calculator assists in several mathematical tasks related to polynomial equations. Firstly, it helps in determining the zeros of a polynomial equation; these are the values for which the polynomial equals zero. Secondly, it can assist in factoring a polynomial equation by providing the polynomial in a product of its factors based on the given roots. Thirdly, it allows you to find the sum of roots of a polynomial equation, which is especially useful for higher degree polynomials. Lastly, it calculates the product of roots of a polynomial equation, a concept that follows from Vieta's formulas for roots of polynomials.
For quadratic equations of the form ax²+bx+c = 0, the roots can be found using the quadratic formula. This is a vital tool in graphing polynomials to understand the behavior of the polynomial curve as the coefficients vary. The quadratic formula helps in identifying the x-intercepts of the graph of the equation, which are particularly the same as its zeros. Furthermore, when working with types of equilibrium problems or any other applications requiring root calculations, it's essential to know how to compute square roots, cube roots, and other higher roots using a calculator.