Quiz about Finding Real and Complex Roots of Polynomials

Question 1

Use the Fundamental Theorem of Algebra to determine the total number of solutions.

Accepted Answer

A

Answer

B

Answer

C

Answer

D

Question 2

Find the zeros of the polynomial.
f(x) = (x-5)(2x+3)(7x-4)(x+6)

Accepted Answer

x= 5, (-3/2), (4/7), -6

Answer

x = 5, (2/3), 6, (7/4)

Answer

x= -5, (3/2), (-4/7), 6

Answer

x= 6, 5, -2/3, -4/7

Question 3

Given one complex zero use the conjugate root theorem to find another.  Zero is 7-5i

Accepted Answer

7+5i

Answer

-7+5i

Answer

7-5i

Answer

-7-5i

Question 4

What are the zeros of the function?

Accepted Answer

-3, -1, 2, 5

Answer

4,1

Answer

3,1,-2,-5

Answer

-2,4

Question 5

Find a polynomial function of degree 3 that has zeroes at
x=1, 2, and 3

Accepted Answer

x³ - 6x²+ 11x - 6

Answer

x³ - 11x²- 6x - 6

Answer

x³ - 6x²- 6x - 6

Answer

x³ - 11x²- 11x - 11

Question 6

The degree of the polynomial determines the number of roots.

Accepted Answer

True

Answer

False

Question 7

All imaginary roots comes in pairs.

Accepted Answer

True

Answer

False

Question 8

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 9

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 10

Write the equation of the quadratic

whose roots are -4, -2.

Accepted Answer

x2+6x+8

Answer

x2-6x+8

Answer

x2-4x-2

Answer

x2-2x-4

Question 11

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 12

How many x-intercepts does x⁴+6x²+9= 0 have?

Accepted Answer

4

Answer

2

Answer

1

Answer

None

Question 13

All zeros containing a square root sign comes in pairs.

Accepted Answer

True

Answer

False

Question 14

Write a polynomial function of degree 4 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 15

A Polynomial of Degree 6 CAN have the following number of imaginary roots:

Accepted Answer

4

Answer

1

Answer

3

Answer

8

Question 16

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

Question 17

What is the degree of a polynomial that has roots of -2, 4i and -4i ?

Accepted Answer

3

Answer

4

Answer

1

Answer

2

Question 18

Is (x-3) a factor of
(x³- 3x²+ 2x + 2)?

Accepted Answer

No

Answer

Yes

Question 19

If 2i is a zero, then

Accepted Answer

-2i is a zero too

Answer

2i repeats twice

Answer

1-2i is a zero too

Answer

0+2i is a zero too

Question 20

What is the least degree of the graph of the above polynomial?

Accepted Answer

5

Answer

3

Answer

4

Answer

Not enough information

Question 21

Question 21.

Accepted Answer

This graph has two imaginary roots because it is a polynomial of degree two.

Answer

This graph has two imaginary roots because it has one hump.

Answer

This graph has two imaginary roots because it touches the x-axis at two points.

Answer

This graph is imaginary because it the graph has shifted up.

Finding Real and Complex Roots of Polynomials

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