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WorksheetsIdentify Zeros of Poly
Total questions: 23
Worksheet time: 3hrs 0mins
Name
Class
Date
1.
Which of the following is a 5th degree trinomial with a leading coefficient of -2?
a)
-2x5 + 3x - 1
b)
5x-2 +3x - 1
c)
-2x5 + 3x4 + 2x3 + x2 - 10
d)
2x + 5
2.
List all possible rational zeros
f(x) = 3x5 - 5x2 + x + 6
a)
1, 2, 3, 6, -1, -2, -3, -6
b)
1/3, 2/3, 1, 2, 3, 6, -1/3, -2/3, -1, -2, -3, -6
c)
1/3, 2/3, 1, 2, 3, 6
3.
What is the degree of the polynomial function
P(x)=3x4 - 7x2 - 2x7 - x + 4?
a)
4
b)
7
c)
2
d)
1
4.
The polynomial
f(x) = 5x4 + 2x3 + 2x − 7 can have, at most, how many solutions?
f(x) = 5x4 + 2x3 + 2x − 7 can have, at most, how many solutions?
a)
5
b)
4
c)
3
d)
2
5.
a)
2
b)
1
c)
4
d)
None
6.
State the possible number of positive real zeros, negative real zeros, and imaginary zeros of the function f(x)=-4x4-2x3-12x2-x-23.
a)
0 positive
4 or 2 negative
0 or 4 imaginary
4 or 2 negative
0 or 4 imaginary
b)
0 positive
4,2, or 0 negative
4, 2, or 0 imaginary
4,2, or 0 negative
4, 2, or 0 imaginary
c)
0 positive
1 negative
3 imaginary
1 negative
3 imaginary
d)
2 or 0 positive
2 or 0 negative
4, 2, or 0 imaginary
2 or 0 negative
4, 2, or 0 imaginary
7.
State the number of REAL ZEROS for the function:
f(x) = 2x4 + 19x2 + 24
a)
4, 2, 0
b)
4, 2
c)
0
d)
4
8.
State the possible number of IMAGINARY ZEROS for the function:
f(x) = 2x4 + 19x2 + 24
a)
4, 2, 0
b)
4, 0
c)
0
d)
4
9.
A polynomial function with rational coefficients of degree 4 MUST have at least 1 real zero.
a)
True
b)
False
10.
A polynomial function with rational coefficients of degree 3 MUST have at least 1 real zero.
a)
True
b)
False
11.
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
12.
Which of the following is a COMPLETE list of all possible Rational Zeros?
f(x) = 2x3 + 5x2 - 9x + 5
f(x) = 2x3 + 5x2 - 9x + 5
a)
±1, 5, 1/2, 5/2
b)
±1, 2, 5, 1/2, 5/2
c)
±1, 5
d)
±1, 2, 5, 1/2, 5/2, 2/5
13.
Find all rational zeros, one zero has been given.
f(x) = x3-5x2-2x+24; -2
f(x) = x3-5x2-2x+24; -2
a)
-2,1,0
b)
-2,-3,-4
c)
4,3,-2
d)
0,0,0
14.
Find all rational zeros, one zero has been given.
f(x) = x3-5x2-2x+24; -2
f(x) = x3-5x2-2x+24; -2
a)
-2,1,0
b)
-2,-3,-4
c)
4,3,-2
d)
0,0,0
15.
Find all rational zeros, one zero has been given.
f(x) = 2x3+5x2-6x-9; -3
f(x) = 2x3+5x2-6x-9; -3
a)
-1,-3,-3
b)
-1,-3,3/2
c)
3,3,3
d)
-3,2/3,-1
16.
Find all zeros. One zero has been given.
f(x) = x4 + 8x3 + 14x2 - 8x - 15; x = -5
f(x) = x4 + 8x3 + 14x2 - 8x - 15; x = -5
a)
-2,1,-1,-5
b)
-3,1,-1,-5
c)
3,-3,4,0
d)
-1,1-5,3
17.
Write a polynomial equation of least degree with roots of -3, -2i, 2i.
a)
(x+3)(x + 2i)(x - 2i) = 0
b)
x3-3x2+4x-12=0
c)
(x+3)(x2+4)=0
d)
x3+3x2+4x+12=0
18.
Find the roots of x4-10x2+9=0
a)
-3, -i, i, 3
b)
-3i, -1, 1, 3i
c)
-3, 3
d)
-3, -1, 1, 3
19.
Determine whether 3 is a root of a4-13a2+12a=0
a)
yes
b)
no
20.
Factor: x6-x4-25x2+25=0
a)
(3x-1)(x+1)(x2-5)(3x2+5)=0
b)
(x-1)(x+1)(x2-5)(x2+5)=0
c)
x(x-1)(x2-5)(x2+5)=0
d)
(x-1)(x+3)(x2-5)(2x2+5)=0
21.
Find all real solutions of the polynomial equation x3 - 3x2 - 2x + 4 = 0
a)
x = -1, 1 ± √5
b)
x = 1, 1 + √5
c)
x = 2, 1 ± √5
d)
x = 1, 1 ± √5
22.
if f(x) = 3x2 -9x -20, find the value of f(5) using synthetic division.
a)
0
b)
10
c)
15
d)
-7
23.
State the possible number of positive real zeros, negative real zeros, and imaginary zeros of the function f(x)=-4x4-2x3-12x2-x-23.
a)
0 positive
4 or 2 negative
0 or 4 imaginary
4 or 2 negative
0 or 4 imaginary
b)
0 positive
4,2, or 0 negative
4, 2, or 0 imaginary
4,2, or 0 negative
4, 2, or 0 imaginary
c)
0 positive
1 negative
3 imaginary
1 negative
3 imaginary
d)
2 or 0 positive
2 or 0 negative
4, 2, or 0 imaginary
2 or 0 negative
4, 2, or 0 imaginary
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