The Rational Roots Theorem Answers

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According to the Rational Root Theorem, the following are potential roots of f(x) = 60x2 – 57x – 18., , 3, 6Which is an actual root of f(x)?

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A
Negative six-fifths
Option A
B
Negative one-fourths
Option B
C
3
D
6
2
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According to the Rational Root Theorem, is a potential rational root of which function?

Question illustration
A
f(x) = 24x7 + 3x6 + 4x3 – x – 28
B
f(x) = 28x7 + 3x6 + 4x3 – x – 24
C
f(x) = 30x7 + 3x6 + 4x3 – x – 56
D
f(x) = 56x7 + 3x6 + 4x3 – x – 30
3

According to the Rational Root Theorem, the following are potential roots of f(x) = 2x2 + 2x – 24.–4, –3, 2, 3, 4Which are actual roots of f(x)?

A
–4 and 3
B
–4, 2, and 3
C
–3 and 4
D
–3, 2, and 4
4

According to the Rational Root Theorem, which statement about f(x) = 66x4 – 2x3 + 11x2 + 35 is true?

A
Any rational root of f(x) is a factor of 35 divided by a factor of 66.
B
Any rational root of f(x) is a multiple of 35 divided by a multiple of 66.
C
Any rational root of f(x) is a factor of 66 divided by a factor of 35.
D
Any rational root of f(x) is a multiple of 66 divided by a multiple of 35.
5

According to the Rational Root Theorem, what are all the potential rational roots of f(x) = 9x4 – 2x2 – 3x + 4?

A
, , , , , 1, , 2, 4
Option A
B
, , , 1, , , 3, , 9
Option B
C
, , , , , 1, , 2, 4
Option C
D
, , , 1, , , 3, , 9
Option D
6

According to the Rational Root Theorem, which number is a potential root of f(x) = 9x8 + 9x6 – 12x + 7?

A
0
B
One-seventh
Option B
C
2
D
Seven-thirds
Option D
7

The graph of f(x) = x6 – 2x4 – 5x2 + 6 is shown below. How many roots of f(x) are rational numbers?

Question illustration
A
1
B
2
C
4
D
6
8

What are all the rational roots of the polynomial f(x) = 20x4 + x3 + 8x2 + x – 12?

A
and
Option A
B
and
Option B
C
–1, , , and 1
Option C
D
–1, , , and 1
Option D
9

The graph of f(x) = 2x3 – 19x2 + 57x – 54 is shown below. How many roots of f(x) are rational numbers?

Question illustration
A
0
B
1
C
2
D
3
10

According to the Rational Roots Theorem, which statement about f(x) = 25x7 – x6 – 5x4 + x – 49 is true?

A
Any rational root of f(x) is a multiple of –49 divided by a multiple of 25.
B
Any rational root of f(x) is a multiple of 25 divided by a multiple of –49.
C
Any rational root of f(x) is a factor of –49 divided by a factor of 25.
D
Any rational root of f(x) is a factor of 25 divided by a factor of –49.

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