Which of the values shown are potential roots of f(x) = 3x3 â€"" 13x2 â€"" 3x 45? Select all that apply.
Answers
The potential roots of the function are, [tex]\pm1, \ \pm3, \ \pm5, \ \pm9,\ \pm15, \ \pm45,\ \pm \dfrac{1}{3},\ \pm \dfrac{5}{3}[/tex]
And the accurate root is 3 it can be determined by using rules of the rational root equation.
Given that,Function; [tex]\rm f(x) = 3x^3 - 13x^2 -3x + 45[/tex]
We have to determine,Which of the values shown are potential roots of the given equation?
According to the question,Potential roots of the polynomial are all possible roots of f(x).
[tex]\rm f(x) = 3x^3 - 13x^2 -3x + 45[/tex]
Using rational root theorem test. We will find all the possible or potential roots of the polynomial.
[tex]\rm p=\dfrac{All\ the \ positive}{Negative\ factors \ of\ 45}[/tex]
[tex]\rm q=\dfrac{All\ the \ positive}{Negative\ factors \ of\ 3}[/tex]
The factor of the term 45 are,
[tex]\pm1, \ \pm3, \ \pm5, \ \pm9,\ \pm15, \ \pm45[/tex]
And The factor of 3 are,
[tex]\pm1, \ \pm3[/tex]
All the possible roots are,
[tex]\dfrac{p}{q} = \pm1, \ \pm3, \ \pm5, \ \pm9,\ \pm15, \ \pm45,\ \pm \dfrac{1}{3},\ \pm \dfrac{5}{3}[/tex]
Now check for all the rational roots which are possible for the given function,
[tex]\rm f(x) = 3x^3 - 13x^2 -3x + 45\\\\ f(1) = 3(1)^3 - 13(1)^2 -3(1) + 45 = 3-13-3+45 = 32\neq 0\\\\ f(-1) = 3(-1)^3 - 13(-1)^2 -3(-1) + 45 =- 3-13+3+45 = 32\neq 0\\\\ f(3) = 3(3)^3 - 13(3)^2 -3(3) + 45 = 81-117-9+45 =0\\\\ f(-3) = 3(-3)^3 - 13(-3)^2 -3(-3) + 45 = -81+117+9+45 =-144\neq 0[/tex]
Therefore, x = 3 is the potential root of the given function.
Hence, The potential roots of the function are, [tex]\pm1, \ \pm3, \ \pm5, \ \pm9,\ \pm15, \ \pm45,\ \pm \dfrac{1}{3},\ \pm \dfrac{5}{3}[/tex].
For more details about Potential roots refer to the link given below.
https://brainly.com/question/25873992
Answer: ALL OF THEM
Step-by-step explanation:
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Therefore your answer is 6q+2
Hope this helps :)
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Step-by-step explanation:
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Answer:
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Step-by-step explanation:
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If m∠2=4x+7 and m∠7=5x-13, find x.
Answers
Answer:
x =20
Step-by-step explanation:
m∠2 ≅ m∠6 because they are corresponding angles
m∠6 ≅ m∠7 because they are vertical angles
∴ m∠2 ≅ m∠7 by substitution
4x+7 = 5x-13
7 = x-13
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The value of x is 20.
What are vertically opposite angles?Vertical angles are angles opposite each other where two lines cross.
What are corresponding angles?Any pair of angles each of which is on the same side of one of two lines cut by a transversal and on the same side of the transversal are corresponding angles.
According to the given question.
We have
m ∠2 = 4x + 7
and m ∠7 = 5x - 13
From the given figure we can say that
m ∠7 = m ∠6...(i) (because they are vertically opposite angles)
and m ∠6 = m ∠2...(ii) ( corresponding angles)
From (i) and (ii)
m ∠7 = m ∠2
⇒ [tex]5x - 13 = 4x + 7[/tex]
⇒ [tex]5x - 4x = 7 +1 3[/tex]
⇒ [tex]x = 20[/tex]
Hence, the value of x is 20.
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Please help with the steps to get the answer. Thank you.
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Answers
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Answers
Answer:
648
Step-by-step explanation:
Running this in Python, with the code as follows,
import math
cur_numbers = [0] * 3
num = 0
for i in range(100, 1000):
cur_numbers[2] = i % 10
i = math.floor(i/10)
cur_numbers[1] = i % 10
i = math.floor(i/10)
cur_numbers[0] = i % 10
if(len(set(cur_numbers)) == 3):
num += 1
print(cur_numbers)
print(num), we get 648 as our answer.
Another way to solve this is as follows:
There are 9 possibilities for the hundreds digit (1-9). Then, there are 10 possibilities for the tens digit, but we subtract 1 because it can't be the 1 same digit as the hundreds digit. For the ones digit, there are 10 possibilities, but we subtract 1 because it can't be the same as the hundreds digit and another 1 because it can't be the same as the tens digit. Multiplying these out, we have
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Hope you could get an idea from here.
Doubt clarification - use comment section.
[tex]\\ \sf\longmapsto 3+√-12[/tex]
[tex]\\ \sf\longmapsto 3+√12i[/tex]
[tex]\\ \sf\longmapsto 3+√2(2)(3)i[/tex]
[tex]\\ \sf\longmapsto 3+2√3i[/tex]
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Answers
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Answers
Answer:
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Answer:
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Answers
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Answers
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1.
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+
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Answer:
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Step-by-step explanation:
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Step-by-step explanation:
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