Imaginary Zeros For Polynomial Functions. If you re given a polynomial like this it s really easy to find the zeros of the function because each of these factors contributes a 0. For a polynomial f x and a constant c a.
If a ib is an imaginary zero of p x the conjugate a bi is also a zero of p x. Remainder theorem if a polynomial f x is divided by x k then the remainder is equal to the value f k. Dividing by x 1 x 1 gives a remainder of 0 so 1 is a zero of the function.
We know that the real zero of this polynomial is 3 so one of the factors must be.
The possible rational zeros of a polynomial function have the form frac p q where p is a factor of the constant term and q is a factor of the leading coefficient. For a polynomial f x and a constant c a. You re generally not going to get a problem this easy. Let s begin with 1.