AnswersAZ-Common Core Algebra II AThe Rational Roots Theorem

The Rational Roots Theorem Answers

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Yuri thinks that is a root of the following function.q(x) = 6x3 + 19x2 – 15x – 28Explain to Yuri why cannot be a root.

Answer:

According to the Rational Root Theorem, potential rational roots must be in the form p/q, where p is a factor of the constant term (28) and q is a factor of the leading coefficient (6). Since 3 is not a factor of 28 and 4 is not a factor of 6, 3/4 cannot be a rational root. Additionally, substituting 3/4 into the function for x does not result in 0, and dividing the polynomial by (x 3/4) would result in a nonzero remainder, confirming that 3/4 is not a root.

25

No, this polynomial has complex roots.No, this polynomial has irrational roots.No, this polynomial has irrational and complex roots.Yes.

A
No, this polynomial has complex roots.
B
No, this polynomial has irrational roots.
C
No, this polynomial has irrational and complex roots.
D
Yes.
29

Question text not available

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30

⇒ -5

Answer:

answer

31

Did you include the following in your response?

A
According to the rational root theorem, potential rational roots must be in theform where p is a factor of the constant term and q is a factor of the leading coefficient.
Option A
B
3 is not a factor of 28, and 4 is not a factor of 6. So, does not satisfy the rational root theorem.
Option B
C
Substituting in for x does not result in 0. The remainder is not 0 when dividing by x –
Option C
32

No, this polynomial has complex roots.No, this polynomial has irrational roots.No, this polynomial has irrational and complex roots.Yes.

A
No, this polynomial has complex roots.
B
No, this polynomial has irrational roots.
C
No, this polynomial has irrational and complex roots.
D
Yes.
35

Question text not available

Answer not available
36

⇒ 1

Answer:

answer

38

–16✔ –202

A
–16
B
–2
C
0
D
2
39

⇒ -5

Answer:

answer

40

⇒ -12

Answer:

answer

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