Final answer:
To find the polynomial equation using a calculator, identify the zeros, form binomial terms for each, multiply these terms to get the factored form, and then expand if necessary. The degree is determined by the highest exponent on x, which corresponds to the total number of zeros.
Step-by-step explanation:
To determine the polynomial equation based on its degree and zeros using a calculator, you would follow these steps:
- First, identify the zeros of the polynomial. These are the x-values where the polynomial intersects with the x-axis (y=0).
- For each zero, if it is a real number a, create a binomial term (x - a). If the zero is complex or repeated, ensure to account for multiplicity and complex conjugates.
- Next, multiply all the binomial terms together. This product is the polynomial function in its factored form.
- If required, expand the product to find the polynomial in standard form by distributing and combining like terms.
The degree of the polynomial is the highest exponent of x in the polynomial, and it is equal to the number of zeros, counting multiplicity.