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Worksheet by Kuta Software LLC
Kuta Software - Infinite Precalculus
Polynomials and Conjugate Roots
Name___________________________________
Date________________ Period____
A polynomial function with rational coefficients has the follow zeros. Find all additional zeros.
1) , i
2)
, 
3)  mult. 2,  4)  , 
5) i,
6) i, i, i
Write a polynomial function of least degree with integral coefficients that has the given zeros.
7)
, ,
8) , i
9) mult. 3
10) , 
11) , 12)   mult. 2,  
13) i mult. 2
14)
, i
Critical thinking questions:
15) Explain why it makes sense that a
third-degree polynomial must have at least
one rational zero.
16) Write a polynomial function of degree ten
that has two imaginary roots.
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Worksheet by Kuta Software LLC
Kuta Software - Infinite Precalculus
Polynomials and Conjugate Roots
Name___________________________________
Date________________ Period____
A polynomial function with rational coefficients has the follow zeros. Find all additional zeros.
1) , i
i
2)
, 

3)  mult. 2, 

4)  , 
 , 
5) i,
i, 
6) i, i, i
i
Write a polynomial function of least degree with integral coefficients that has the given zeros.
7)
, ,
f
(
x
)
x
x
x
8) , i
f
(
x
)
x
x
x
9) mult. 3
f
(
x
)
x
x
x
10) , 
f
(
x
)
x
x
x
11) ,
f
(
x
)
x
x
x
12)  
mult. 2,  
f
(
x
)
x
x
x
x
13) i mult. 2
f
(
x
)
x
x

14)
, i
f
(
x
)
x
x
x
Critical thinking questions:
15) Explain why it makes sense that a
third-degree polynomial must have at least
one rational zero.
It must go from to  so it must
cross the x-axis.
16) Write a polynomial function of degree ten
that has two imaginary roots.
f
(
x
)

(
x

)
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