Grade 10 Exam > Grade 10 Questions > What real number that should be added to the ...
Start Learning for Free
What real number that should be added to the polynomial f(x) = 81x2 - 31, so that it is exactly divisible by 9x + 1?
- a)40
- b)10
- c)30
- d)20
Correct answer is option 'C'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Most Upvoted Answer
What real number that should be added to the polynomial f(x) = 81x2- 3...
81x2 - 31 is exactly divisible by 9x + 1
Hence, on dividing 81x2 - 31 by 9x + 1
We get, 9x - 1 as quotient and remainder as -30.
So if we add 30 to 81x2 - 31, it will be exactly divisible by 9x + 1.
Hence, on dividing 81x2 - 31 by 9x + 1
We get, 9x - 1 as quotient and remainder as -30.
So if we add 30 to 81x2 - 31, it will be exactly divisible by 9x + 1.
Free Test
FREE
| Start Free Test |
Community Answer
What real number that should be added to the polynomial f(x) = 81x2- 3...
Understanding the Problem:
To find the real number that needs to be added to the polynomial to make it exactly divisible by 9x + 1.
Given Polynomial:
f(x) = 81x^2 - 31
Divisor:
9x + 1
Approach:
We need to find the real number 'a' such that when added to the given polynomial, the resulting polynomial is divisible by 9x + 1.
- We know that for a polynomial to be divisible by 9x + 1, the remainder should be zero when the polynomial is divided by 9x + 1.
- We can use the remainder theorem to find the value of 'a'.
Using Remainder Theorem:
- If f(x) is divisible by (x - p), then f(p) = 0.
- Here, we need to find the value of 'a' such that f(x) + a is divisible by 9x + 1.
- So, we substitute x = -1/9 in the polynomial f(x) + a and equate it to zero to find 'a'.
Calculations:
f(-1/9) + a = 0
81(-1/9)^2 - 31 + a = 0
81/81 - 31 + a = 0
1 - 31 + a = 0
-30 + a = 0
a = 30
Conclusion:
Therefore, the real number that should be added to the polynomial f(x) = 81x^2 - 31 so that it is exactly divisible by 9x + 1 is 30.
To find the real number that needs to be added to the polynomial to make it exactly divisible by 9x + 1.
Given Polynomial:
f(x) = 81x^2 - 31
Divisor:
9x + 1
Approach:
We need to find the real number 'a' such that when added to the given polynomial, the resulting polynomial is divisible by 9x + 1.
- We know that for a polynomial to be divisible by 9x + 1, the remainder should be zero when the polynomial is divided by 9x + 1.
- We can use the remainder theorem to find the value of 'a'.
Using Remainder Theorem:
- If f(x) is divisible by (x - p), then f(p) = 0.
- Here, we need to find the value of 'a' such that f(x) + a is divisible by 9x + 1.
- So, we substitute x = -1/9 in the polynomial f(x) + a and equate it to zero to find 'a'.
Calculations:
f(-1/9) + a = 0
81(-1/9)^2 - 31 + a = 0
81/81 - 31 + a = 0
1 - 31 + a = 0
-30 + a = 0
a = 30
Conclusion:
Therefore, the real number that should be added to the polynomial f(x) = 81x^2 - 31 so that it is exactly divisible by 9x + 1 is 30.
Attention Grade 10 Students!
To make sure you are not studying endlessly, EduRev has designed Grade 10 study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Grade 10.
|
Explore Courses for Grade 10 exam
|
|
Similar Grade 10 Doubts
Top Courses for Grade 10View all
What real number that should be added to the polynomial f(x) = 81x2- 31, so that it is exactly divisible by 9x + 1?a)40b)10c)30d)20Correct answer is option 'C'. Can you explain this answer?
Question Description
What real number that should be added to the polynomial f(x) = 81x2- 31, so that it is exactly divisible by 9x + 1?a)40b)10c)30d)20Correct answer is option 'C'. Can you explain this answer? for Grade 10 2024 is part of Grade 10 preparation. The Question and answers have been prepared according to the Grade 10 exam syllabus. Information about What real number that should be added to the polynomial f(x) = 81x2- 31, so that it is exactly divisible by 9x + 1?a)40b)10c)30d)20Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Grade 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What real number that should be added to the polynomial f(x) = 81x2- 31, so that it is exactly divisible by 9x + 1?a)40b)10c)30d)20Correct answer is option 'C'. Can you explain this answer?.
What real number that should be added to the polynomial f(x) = 81x2- 31, so that it is exactly divisible by 9x + 1?a)40b)10c)30d)20Correct answer is option 'C'. Can you explain this answer? for Grade 10 2024 is part of Grade 10 preparation. The Question and answers have been prepared according to the Grade 10 exam syllabus. Information about What real number that should be added to the polynomial f(x) = 81x2- 31, so that it is exactly divisible by 9x + 1?a)40b)10c)30d)20Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Grade 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What real number that should be added to the polynomial f(x) = 81x2- 31, so that it is exactly divisible by 9x + 1?a)40b)10c)30d)20Correct answer is option 'C'. Can you explain this answer?.
Solutions for What real number that should be added to the polynomial f(x) = 81x2- 31, so that it is exactly divisible by 9x + 1?a)40b)10c)30d)20Correct answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for Grade 10.
Download more important topics, notes, lectures and mock test series for Grade 10 Exam by signing up for free.
Here you can find the meaning of What real number that should be added to the polynomial f(x) = 81x2- 31, so that it is exactly divisible by 9x + 1?a)40b)10c)30d)20Correct answer is option 'C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
What real number that should be added to the polynomial f(x) = 81x2- 31, so that it is exactly divisible by 9x + 1?a)40b)10c)30d)20Correct answer is option 'C'. Can you explain this answer?, a detailed solution for What real number that should be added to the polynomial f(x) = 81x2- 31, so that it is exactly divisible by 9x + 1?a)40b)10c)30d)20Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of What real number that should be added to the polynomial f(x) = 81x2- 31, so that it is exactly divisible by 9x + 1?a)40b)10c)30d)20Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice What real number that should be added to the polynomial f(x) = 81x2- 31, so that it is exactly divisible by 9x + 1?a)40b)10c)30d)20Correct answer is option 'C'. Can you explain this answer? tests, examples and also practice Grade 10 tests.
|
|
Explore Courses for Grade 10 exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup