Learn how to write the equation of a polynomial when given complex zeros. Recall that a polynomial is an expression of the form ax^n + bx^(n-1) + . . . + k, where a, b, and k are constants and the exponents are positive integers. The zeros of a polynomial are the values of x for which the value of the polynomial is zero. Also recall that when a complex number is a zero to a polynomial, the conjugate of the complex number will also be a zero to the polynomial.
To write the equation of a polynomial, we write the given zeros in factor form and expand the product of the factors. Thus, given a, b, . . . as zeros to a polynomial, we write the equation of the polynomial by expanding the factors (x - a)(x - b) . . . = 0