Finding Equations Given Complex Roots

All imaginary roots comes in pairs.

• True
• False

Write the polynomial in standard form given the following zeros. x = -2, 1, 4

• f(x) = (x+2)(x-1)(x-4)

• f(x) =x³ - 3x² - 6x + 8

• f(x) = x³ + 8

• f(x) = x³ - 3x² + 8

Which of the following would be a root with 3i?

• 3i²

• -3i

• 3i

• -3i²

Which of the following would be the correct factored form with roots 2, 5i, and 6?

• (x-6)(x-2)(x+5i)(x-5i)

• (x+6)(x+2)(x+5i)

• (x-6)(x-2)(x-5i)

• (x+6)(x+2)(x-5i)

If a+bi is a root of a polynomial, then _______ is also a root.

• i²

• a-bi

• a+bi

• -i²

Use the Complex Conjugate Root Theorem to state another complex solution. Given that -2-5i is a root. 

• -2-5i
• -2+5i
• 2+5i
• 5i

Write a polynomial function of least degree with integral coefficients that has the given zeros.

• A
• B
• C
• D

Find a polynomial function of degree 3 with zeros 3i and -2.

• P(x) = x³+2x²+9x+11
• P(x) = x³-2x²+9x+18
• P(x) = x³+2x²+9x+18
• P(x) = x²-3ix+2x-6i

Write a polynomial function of least degree with integral coefficients that has the given zeros.

• A
• B
• C
• D

Write a polynomial function of least degree with integral coefficients that has the given zeros.

• A
• B
• C
• D