Final answer:
To find the zeros of the given polynomial, we can start by using the given complex zero and applying the conjugate zero theorem. Then, we can use polynomial division or synthetic division to divide the given polynomial by these zeros. Solving the resulting quadratic equation will give us the remaining real zero.
Step-by-step explanation:
To find the zeros of the given polynomial, we can start by using the given complex zero and applying the conjugate zero theorem. Since 2 - i is a zero, its conjugate 2 + i will also be a zero. Thus, we have two complex zeros: 2 - i and 2 + i.
Next, we can use polynomial division or synthetic division to divide the given polynomial by these zeros. Dividing f(x) by (x - (2 - i)) and (x - (2 + i)) will give us the quotient polynomial, which is a quadratic equation. Solving this quadratic equation will give us the remaining real zero. Let's perform the division and solve.
Step 1: Divide f(x) by (x - (2 - i)) using synthetic division.
Step 2: Divide the resulting quadratic equation by (x - (2 + i)) using synthetic division.
Step 3: Solve the resulting quadratic equation to find the remaining real zero.
To find the zeros of the given polynomial, we can start by using the given complex zero and applying the conjugate zero theorem. Then, we can use polynomial division or synthetic division to divide the given polynomial by these zeros. Solving the resulting quadratic equation will give us the remaining real zero.