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WorksheetsRoots and Turns of Polynomials
Total questions: 23
Worksheet time: 3hrs 40mins
Name
Class
Date
1.
Use the Fundamental Theorem of Algebra to determine the total number of solutions.
a)
A
b)
B
c)
C
d)
D
2.
Find the zeros of the polynomial.
f(x) = (x-5)(2x+3)(7x-4)(x+6)
f(x) = (x-5)(2x+3)(7x-4)(x+6)
a)
x = 5, (2/3), 6, (7/4)
b)
x= -5, (3/2), (-4/7), 6
c)
x= 5, (-3/2), (4/7), -6
d)
x= 6, 5, -2/3, -4/7
3.
Given one complex zero use the conjugate root theorem to find another. Zero is 7-5i
a)
-7+5i
b)
7-5i
c)
-7-5i
d)
7+5i
4.
What are the zeros of the function?
a)
4,1
b)
3,1,-2,-5
c)
-3, -1, 2, 5
d)
-2,4
5.
Find a polynomial function of degree 3 that has zeroes at
x=1, 2, and 3
x=1, 2, and 3
a)
x3 - 6x2 + 11x - 6
b)
x3 - 11x2 - 6x - 6
c)
x3 - 6x2 - 6x - 6
d)
x3 - 11x2 - 11x - 11
6.
Find a polynomial function that has zeroes at
x=1+√2, 1-√2, and 1
x=1+√2, 1-√2, and 1
a)
x3 - 3x2 + x +1
b)
x3 - 3x2 + 3x +1
c)
x3 - x2 + x +3
d)
x3 - 3x2 + 3x +3
7.
The degree of the polynomial determines the number of roots.
a)
True
b)
False
8.
All imaginary roots comes in pairs.
a)
True
b)
False
9.
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)
10.
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
11.
Write the equation of the quadratic
whose roots are -4, -2.
a)
x2-6x+8
b)
x2+6x+8
c)
x2-4x-2
d)
x2-2x-4
12.
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
13.
How many x-intercepts does x4+6x2+9= 0 have?
a)
2
b)
1
c)
4
d)
None
14.
All zeros containing a square root sign comes in pairs.
a)
True
b)
False
15.
What is the conjugate of 2 + √3
a)
2 + √3
b)
2 - √3
c)
-2 + √3
d)
-2 - √3
16.
Write a polynomial function of degree 4 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
17.
A Polynomial of Degree 6 CAN have the following number of imaginary roots:
a)
1
b)
4
c)
3
d)
8
18.
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
19.
What is the degree of a polynomial that has roots of -2, 4i and -4i ?
a)
3
b)
4
c)
1
d)
2
20.
Is (x-3) a factor of
(x3 - 3x2 + 2x + 2)?
(x3 - 3x2 + 2x + 2)?
a)
Yes
b)
No
21.
If 2i is a zero, then
a)
2i repeats twice
b)
-2i is a zero too
c)
1-2i is a zero too
d)
0+2i is a zero too
22.
What is the least degree of the graph of the above polynomial?
a)
3
b)
4
c)
5
d)
Not enough information
23.
a)
This graph has two imaginary roots because it is a polynomial of degree two.
b)
This graph has two imaginary roots because it has one hump.
c)
This graph has two imaginary roots because it touches the x-axis at two points.
d)
This graph is imaginary because it the graph has shifted up.
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