Imaginary Zeros Of Polynomial Functions. F 1 10. Use the rational zero theorem to list all possible rational zeros of the function.
When any complex number with an imaginary component is given as a zero of a polynomial with real coefficients the conjugate must also be a zero of the polynomial. Pageindex 5 find a third degree polynomial with real coefficients that has zeros of 5 and 2i such that f 1 10. This pair of implications is the factor theorem.
When any complex number with an imaginary component is given as a zero of a polynomial with real coefficients the conjugate must also be a zero of the polynomial.
Given a polynomial function latex f latex use synthetic division to find its zeros. If the remainder is 0 the candidate is a zero. Notice written in this form is a factor of we can conclude if is a zero of then is a factor of similarly if is a factor of then the remainder of the division algorithm is 0. For these cases we first equate the polynomial function with zero and form an equation.