Solving Polynomial Equations with Complex Solutions

• A
• B
• C
• D

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.

Solve x²+64 = 0

• 8

• -8, 8

• 8i, -8i

• -8

Tags

TEKS.MATH.A.8A

Which is a solution to (½)x² + 8 = 0

• - 4i

• 16i

• - 16i

• 1

Tags

TEKS.MATH.A.8A

Solve for x:

3x² - 6x + 6 = 0

• x = 1± i

• x = 3, -6

• x = 4.8, 2.7

• Undefined

Tags

TEKS.MATH.A.8A

Solve.
4x² - 7 = -10

• x = ± (3i)/2

• x = ± (i√3)/2

• x = ± (i√3)/4

• x = ± (i√6)/4

Tags

TEKS.MATH.A.8A

Solve -2x² + 4x = 9

• (2 - i√14)/2   ,   (2 + i√14)/2

• (2 - i√-56)/2   ,   (2 + i√-56)/2

• (2 - i√-14)/2   ,   (2 + i√-14)/2

• (2 - √14)/2   ,   (2 + √14)/2

Tags

TEKS.MATH.A.8A

Solve x² = -25

• x = -5

• x = ± 5i

• x = √5

• x = ± 5

Tags

TEKS.MATH.A.8A