Question

Form a polynomial in factored and standard from that has a degree of 3 and zeros: 2 - i, and

1.

Answer 1

• (x - 2 + i)(x - 2 - i)(x - 1)

• x^3 -5x^2 + 9x - 5

Explanation:

In order to have rational polynomial, it has to have 2 + i as third zero.

Polynomial in factored form:

• (x - (2 - i))(x - (2 + i))(x - 1) =
• (x - 2 + i)(x - 2 - i)(x - 1)

Polynomial in standard form:

• (x^2 - 2x - ix - 2x + 4 +2i + ix - 2i -i^2)(x - 1) =
• (x^2 - 4x + 4 + 1)(x - 1) =
• (x^2 - 4x + 5)(x - 1) =
• x^3 - x^2 - 4x^2 + 4x + 5x - 5 =
• x^3 -5x^2 + 9x - 5