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WorksheetsSolving Polynomials with Imaginary
Total questions: 20
Worksheet time: 20mins
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
(a)
Given f(x) , shown above, how many real and imaginary roots does f(x) have?
3 real roots, 0 imaginary roots
2 real roots, 1 imaginary root
1 real root, 2 imaginary roots
0 real roots, 3 imaginary roots
What is the value of x?
10
-10
10i
-10i
Solve for x:
x = {-4, -1}
x = {-1, -4}
x = {2+i, 2-i}
x = {-2+i, -2-i}
Oliver is studying polynomial functions in his mathematics class. He needs to determine which of the following polynomial functions have exactly 5 roots, including all real and imaginary roots. Can you help him?
f(x) = 5x^4 + x^3 - x^2 + x - 5
f(x) = 4x^5 + 3x^4 + 2x^3 + x^2 + x
f(x) = 5x^6 - 5x^4 + 5x^2 - 5
f(x) = 4x^4 - 3x^3 + 2x^2 - 1
Michael is studying polynomial functions and comes across a function P defined by p(x)=(x2+4)(x2−9) . He is curious about the zeros of P. Which of the following correctly describes the zeros of P?
P has exactly two distinct real zeros and no non-real zeros.
P has exactly three distinct real zeros.
P has exactly four distinct real zeros.
P has exactly two distinct real zeros and two non-real zeros.
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
Use the Fundamental Theorem of Algebra to determine the total number of solutions.
A
B
C
D
Given one complex zero use the conjugate root theorem to find another. Zero is 7-5i
-7+5i
7-5i
-7-5i
7+5i
All imaginary roots comes in pairs.
True
False
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)
