Solving Polynomials with Imaginary

Imagine a scenario where Aria is solving a polynomial equation with real coefficients in her math class. She finds that one solution of the equation is in the form (a - bi), where (b ≠ 0). Which of the following expressions must also be a solution according to the complex conjugate root theorem?

• (a + bi)

• (-a + bi)

• (-b + ai)

• (b - ai)

Imagine Mason is analyzing a polynomial function f(x) = x^4 - 12x + 1 as part of his mathematics project. Including all real and imaginary solutions, how many solutions exist for this function?

• 0

• 1

• 2

• 4

During a mathematics competition, Priya is tasked with analyzing the polynomial (x^8 + 2x^5 - x^4 + 6). Which statement is true about this polynomial?

• It has exactly 4 roots, including any repeated roots, that must be real numbers.

• It has exactly 8 roots, including any repeated roots, that must be real numbers.

• It has exactly 4 roots, including any repeated roots, that may be either real or complex numbers.

• It has exactly 8 roots, including any repeated roots, that may be either real or complex numbers.

Imagine Luna is working on a complex project involving polynomial equations. She encounters the equation 7x^4 - 5x^3 + 9x^8 + 10x - 6 = 0. How many solutions, including all real and imaginary solutions, does this equation have?

• 6

• 7

• 8

• 9

• A

• B

• C

• D

• A

• B

• C

• D

• A

• B

• C

• D

• A

• B

• C

• D

Determine the number of IMAGINARY solutions

• 3 real roots, 0 imaginary roots

• 2 real roots, 1 imaginary root

• 1 real root, 2 imaginary roots

• 0 real roots, 3 imaginary roots