Free Printable Complex Roots of Polynomials

1.

Use the Complex Conjugate Root Theorem to state another complex solution. Given that 3+5i is a root.

a)

-3+5i

b)

-3-5i

c)

-5i

d)

3-5i

2.

Use the Complex Conjugate Root Theorem to state another complex solution. Given that -7i is a root.

a)

7i

b)

-7i+1

c)

1-7i

d)

1+7i

3.

What is the total number of roots for the following equation?
ax⁵+ bx⁴+ cx³+ dx²+ ex+ f = y

a)

This equation has 2 roots.

b)

This equation has 4 roots.

c)

This equation has 5 roots.

d)

This equation has no roots.

4.

Which of these is a possible root of the polynomials?
x³ - 6x² - x + 30

a)

0

b)

4

c)

-9

d)

-15

5.

What is another way to say "where a function crosses the x-axis"?

a)

x-intercept

b)

zero

c)

root

d)

all of these.

6.

Write a polynomial with roots at 2 and 3-2i in standard form.

a)

x³- 7x²+ 25x - 21

b)

x³- 8x²+ 25x - 26

c)

- 8x² - 26

d)

x²+ 6ix - 4i

7.

What is the degree of the polynomial:
f(x) = -4x + 5x³ - 2x²

a)

Degree 2

b)

Degree 3

c)

Degree 4

d)

Degree 5

8.

Identify the degree of the polynomial and the sign of the leading coefficient

a)

Leading Coefficient Positive
Degree - Even

b)

Leading Coefficient Positive
Degree - Odd

c)

Leading Coefficient Negative
Degree - Even

d)

Leading Coefficient Negative
Degree - Odd

9.

Find the polynomial equation with given zeros.

a)

x³-x²+4x+4

b)

x³+x²+4x+4

c)

x³-x²-4x+4

d)

x³+x²+4x-4

10.

What does i² equal to?

a)

1

b)

-1

c)

i

d)

-i

11.

What is the conjugate of -8i?

a)

-8i

b)

8i

c)

8

d)

-8

12.

What is the complex conjugate of 3 + √3?

a)

3 - √3

b)

-3 - √3

c)

3 + √3

d)

-3 + √3

13.

All imaginary roots comes in pairs.

a)

True

b)

False

14.

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

a)

f(x) = (x+2)(x-1)(x-4)

b)

f(x) =x³ - 3x² - 6x + 8

c)

f(x) = x³+ 8

d)

f(x) = x³ - 3x² + 8

15.

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

a)

(x-6)(x-2)(x+5i)(x-5i)

b)

(x+6)(x+2)(x+5i)

c)

(x-6)(x-2)(x-5i)

d)

(x+6)(x+2)(x-5i)

16.

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

a)

i²

b)

a-bi

c)

a+bi

d)

-i²

17.

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

a)

-2-5i

b)

-2+5i

c)

2+5i

d)

5i

18.

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

a)

P(x) = x³+2x²+9x+11

b)

P(x) = x³-2x²+9x+18

c)

P(x) = x³+2x²+9x+18

d)

P(x) = x²-3ix+2x-6i

19.

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

-1, 5, -3+2i

a)

x⁴+2x³-16x²-82x-69

b)

x⁴+7x³-16x²-82x-65

c)

x⁴+2x³-16x²-82x-65

d)

x⁴+2x³-16x²-82x-68

20.

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

5, -2i

a)

x³-5x²+4x-20

b)

x³-5x²+4x-23

c)

x³-5x²+4x-19

d)

x³-10x²+4x-20

21.

Factor each polynomial and state the roots. $x^4-12x^2+32=0$

a)

$\left\{2,\ \ 2\sqrt{2}\right\}$

b)

$\left\{2,\ -2,\ 2\sqrt{2}\right\}$

c)

$\left\{2,\ -2,\ \sqrt{8}\right\}$

d)

$\left\{2,-2,\ 2\sqrt{2},-2\sqrt{2}\right\}$

22.

Write a polynomial function of least degree in standard form that has the follow roots.
$-3,\ \sqrt{5}$

a)

$f\left(x\right)=\left(x+3\right)\left(x^2-5\right)$

b)

$f\left(x\right)=\left(x-3\right)\left(x-\sqrt{5}\right)$

c)

$f\left(x\right)=x^3+3x^2-5x-15$

d)

$f\left(x\right)=x^3-3x^2+5x+15$

23.

Find all exact roots. $f\left(x\right)=x^3+7x^2-7x-57$

a)

$\left\{-3,\ -2\ \pm\ \sqrt{23}\right\}$

b)

$\left\{-3,\ -2,\ \pm\sqrt{23}\right\}$

c)

$\left\{3,\ -3,\ 2,\ -2,\ \pm\sqrt{23}\right\}$

d)

$\left\{-3,\ \pm\sqrt{23}\right\}$

24.

What is the conjugate of 2 + √3

a)

2 + √3

b)

2 - √3

c)

-2 + √3

d)

-2 - √3

25.

All zeros containing a square root sign comes in pairs.

a)

True

b)

False

26.

What is the complex conjugate of 3 + √3?

a)

3 - √3

b)

-3 - √3

c)

3 + √3

d)

-3 + √3

27.

Given the polynomial below, how many roots will it have?
$y=x^3+5x^2-9x-2$

a)

2

b)

1

c)

3

d)

0

28.

What is the degree of the following polynomial that has 4 real roots and 2 complex roots?

a)

4

b)

2

c)

8

d)

6

Complex Roots of Polynomials

Total questions: 28

Worksheet time: 2hrs 13mins

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