Quiz about Complex Conjugates and Zeros

Question 1

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

Accepted Answer

3-5i

Answer

-3+5i

Answer

-3-5i

Answer

-5i

Question 2

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

Accepted Answer

7i

Answer

-7i+1

Answer

1-7i

Answer

1+7i

Question 3

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

Accepted Answer

This equation has 5 roots.

Answer

This equation has 2 roots.

Answer

This equation has 4 roots.

Answer

This equation has no roots.

Question 4

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

Accepted Answer

-15

Answer

0

Answer

4

Answer

-9

Question 5

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

Accepted Answer

all of these.

Answer

x-intercept

Answer

zero

Answer

root

Question 6

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

Accepted Answer

x³- 8x²+ 25x - 26

Answer

x³- 7x²+ 25x - 21

Answer

- 8x² - 26

Answer

x²+ 6ix - 4i

Question 7

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

Accepted Answer

Degree 3

Answer

Degree 2

Answer

Degree 4

Answer

Degree 5

Question 8

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

Accepted Answer

Leading Coefficient Negative
Degree - Odd

Answer

Leading Coefficient Positive
Degree - Even

Answer

Leading Coefficient Positive
Degree - Odd

Answer

Leading Coefficient Negative
Degree - Even

Question 9

Find the polynomial equation with given zeros.

Accepted Answer

x³+x²+4x+4

Answer

x³-x²+4x+4

Answer

x³-x²-4x+4

Answer

x³+x²+4x-4

Question 10

What does i² equal to?

Accepted Answer

-1

Answer

1

Answer

i

Answer

-i

Question 11

What is the conjugate of -8i?

Accepted Answer

8i

Answer

-8i

Answer

8

Answer

-8

Question 12

All imaginary roots comes in pairs.

Accepted Answer

True

Answer

False

Question 13

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

Accepted Answer

f(x) =x³ - 3x² - 6x + 8

Answer

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

Answer

f(x) = x³+ 8

Answer

f(x) = x³ - 3x² + 8

Question 14

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

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 15

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

Accepted Answer

a-bi

Answer

i2

Answer

a+bi

Answer

-i2

Question 16

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

Accepted Answer

-2+5i

Answer

-2-5i

Answer

2+5i

Answer

5i

Question 17

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

Accepted Answer

P(x) = x³+2x²+9x+18

Answer

P(x) = x³+2x²+9x+11

Answer

P(x) = x³-2x²+9x+18

Answer

P(x) = x²-3ix+2x-6i

Question 18

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

-1, 5, -3+2i

Accepted Answer

x⁴+2x³-16x²-82x-65

Answer

x⁴+2x³-16x²-82x-69

Answer

x⁴+7x³-16x²-82x-65

Answer

x⁴+2x³-16x²-82x-68

Question 19

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

5, -2i

Accepted Answer

x³-5x²+4x-20

Answer

x³-5x²+4x-23

Answer

x³-5x²+4x-19

Answer

x³-10x²+4x-20

Question 20

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

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 21

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

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 22

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

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 23

All zeros containing a square root sign comes in pairs.

Accepted Answer

True

Answer

False

Question 24

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

Accepted Answer

Answer

Answer

Answer

Question 25

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

Accepted Answer

6

Answer

4

Answer

2

Answer

8

Create a free account and access millions of resources

Similar Resources on Wayground

Popular Resources on Wayground

Discover more resources for Mathematics