Quadratic in Form Polynomials Answers

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1
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How many x-intercepts appear on the graph of this polynomial function?

Question illustration
A
1 x-intercept
B
2 x-intercepts
C
3 x-intercepts
D
4 x-intercepts
2
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Trevor is studying a polynomial function f(x). Three given roots of f(x) are –7, 2i, and 7. Trevor concludes that f(x) must be a polynomial with degree 3. Which statement is true?

A
Trevor is correct.
B
Trevor is not correct because –2i must also be a root.
C
Trevor is not correct there cannot be an odd number of roots.
D
Trevor is not correct because there cannot be both rational and complex roots.
3

Two roots of a third degree polynomial function f(x) are –4 and 4. Which statement describes the number and nature of all roots for this function?

A
f(x) has three imaginary roots.
B
f(x) has three real roots.
C
f(x) has two real roots and two imaginary roots.
D
f(x) has three real roots and one imaginary root.
5

According to the Fundamental Theorem of Algebra, which polynomial function has exactly 11 roots?

A
f (x) = (x minus 1) (x + 1) Superscript 11
Option A
B
f (x) = (x + 2) cubed (x squared minus 7 x + 3) Superscript 4
Option B
C
f (x) = (x Superscript 5 Baseline + 7 x + 14) Superscript 6
Option C
D
f (x) = 11 x Superscript 5 Baseline + 5 x + 25
Option D
7

How many x-intercepts appear on the graph of this polynomial function?

Question illustration
A
1 x-intercept
B
2 x-intercepts
C
3 x-intercepts
D
4 x-intercepts
9

Which of the following statements must be true about the polynomial function f(x)?

A
If is a root of f(x), then is also a root of f(x).
Option A
B
If 1 + 13i is a root of f(x), then 1 – 13i is also a root of f(x).
C
If 13 is a root of f(x), then –13 is also a root of f(x).
D
If –13 + i is a root of f(x), then 13 + i is also a root of f(x).
10

Patricia is studying a polynomial function f(x). Three given roots of f(x) are , 3 + 4i, and 10. Patricia concludes that f(x) must be a polynomial with degree 4. Which statement is true?

Question illustration
A
Patricia is correct because must be a root.
Option A
B
Patricia is correct because 3 – 4i must be a root.
C
Patricia is not correct because both 3 – 4i and must be roots.
Option C
D
Patricia is not correct because both 3 – 4i and must be roots.
Option D

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