AnswersINMT3 Integrated Math 3 Sem 1 26-27Writing Polynomial Functions from Complex Roots

Writing Polynomial Functions from Complex Roots Answers

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If a polynomial function, f(x), with rational coefficients has roots 3 and , what must also be a root of f(x)?

Question illustration
A
Negative StartRoot 7 EndRoot
Option A
B
i StartRoot 7 EndRoot
Option B
C
–3
D
3i
2
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What is the polynomial function of lowest degree with lead coefficient 1 and roots i, –2, and 2?

A
f(x) = x3 – x2 – 4x + 4
B
f(x) = x4 – 3x2 – 4
C
f(x) = x4 + 3x2 – 4
D
f(x) = x3 + x2 – 4x – 4
3

If a polynomial function f(x) has roots –8, 1, and 6i, what must also be a root of f(x)?

A
–6
B
–6i
C
6 – i
D
6
4

If a polynomial function f(x) has roots –9 and 7 – i, what must be a factor of f(x)?

A
(x – (7 + i))
B
(x – (–7 – i))
C
(x + (7 + i))
D
(x + (7 – i))
5

What must be a factor of the polynomial function f(x) graphed on the coordinate plane below?

Question illustration
A
x – 3
B
x – 1
C
x + 1
D
x + 3
6

Which polynomial function has a leading coefficient of 1 and roots 2i and 3i with multiplicity 1?

A
f(x) = (x – 2i)(x – 3i)
B
f(x) = (x + 2i)(x + 3i)
C
f(x) = (x – 2)(x – 3)(x – 2i)(x – 3i)
D
f(x) = (x + 2i)(x + 3i)(x – 2i)(x – 3i)
7

Which polynomial function has a leading coefficient of 3 and roots –4, i, and 2, all with multiplicity 1?

A
f(x) = 3(x + 4)(x – i)(x – 2)
B
f(x) = (x – 3)(x + 4)(x – i)(x – 2)
C
f(x) = (x – 3)(x + 4)(x – i)(x + i)(x – 2)
D
f(x) = 3(x + 4)(x – i)(x + i)(x – 2)
8

Which polynomial function has a leading coefficient of 1 and roots (7 + i) and (5 – i) with multiplicity 1?

A
f(x) = (x + 7)(x – i)(x + 5)(x + i)
B
f(x) = (x – 7)(x – i)(x – 5)(x + i)
C
f(x) = (x – (7 – i))(x – (5 + i))(x – (7 + i))(x – (5 – i))
D
f(x) = (x + (7 – i))(x + (5 + i))(x + (7 + i))(x + (5 – i))
9

What must be a factor of the polynomial function f(x) graphed on the coordinate plane below?

Question illustration
A
x – 3
B
x – 1
C
x + 1
D
x + 3
10

Which polynomial function could be represented by the graph below?

Question illustration
A
f(x) = x2 – 6x + 8
B
f(x) = 3x2 – 18x + 24
C
f(x) = x2 + 6x + 8
D
f(x) = 3x2 + 18x + 24

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