JEE Exam > JEE Questions > An unknown polynomial yields a remainder of 2...
Start Learning for Free
An unknown polynomial yields a remainder of 2 upon division by x − 1, and a remainder of 1 upon division by x − 2. If this polynomial is divided by (x − 1)(x − 2), then the remainder is
- a)2
- b)3
- c)− x + 3
- d)x + 1
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
An unknown polynomial yields a remainder of 2 upon division by x &minu...
We can solve this problem by using the Remainder Theorem, which states that if a polynomial is divided by (x - a), the remainder is the value of the polynomial evaluated at x = a.
In this case, we know that the polynomial yields a remainder of 2 when divided by x, so we can write:
f(x) = q(x) * x + 2
where f(x) is the unknown polynomial, q(x) is the quotient polynomial, and 2 is the remainder.
Now, we can use the Remainder Theorem again to find the value of f(0), which is the constant term of the polynomial. We know that when x = 0, the remainder is 2, so we have:
f(0) = q(0) * 0 + 2 = 2
Therefore, the unknown polynomial has a constant term of 2. We still don't know the degree or the coefficients of the polynomial, but we can say that the general form of the polynomial is:
f(x) = ax^n + bx^(n-1) + ... + 2
where a, b, and the other coefficients are unknown.
In this case, we know that the polynomial yields a remainder of 2 when divided by x, so we can write:
f(x) = q(x) * x + 2
where f(x) is the unknown polynomial, q(x) is the quotient polynomial, and 2 is the remainder.
Now, we can use the Remainder Theorem again to find the value of f(0), which is the constant term of the polynomial. We know that when x = 0, the remainder is 2, so we have:
f(0) = q(0) * 0 + 2 = 2
Therefore, the unknown polynomial has a constant term of 2. We still don't know the degree or the coefficients of the polynomial, but we can say that the general form of the polynomial is:
f(x) = ax^n + bx^(n-1) + ... + 2
where a, b, and the other coefficients are unknown.
Community Answer
An unknown polynomial yields a remainder of 2 upon division by x &minu...
Attention JEE Students!
To make sure you are not studying endlessly, EduRev has designed JEE study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in JEE.
|
Explore Courses for JEE exam
|
|
Similar JEE Doubts
Top Courses for JEEView all
An unknown polynomial yields a remainder of 2 upon division by x − 1, and a remainder of 1 upon division by x − 2. If this polynomial is divided by (x − 1)(x − 2), then the remainder isa)2b)3c)− x + 3d)x + 1Correct answer is option 'C'. Can you explain this answer?
Question Description
An unknown polynomial yields a remainder of 2 upon division by x − 1, and a remainder of 1 upon division by x − 2. If this polynomial is divided by (x − 1)(x − 2), then the remainder isa)2b)3c)− x + 3d)x + 1Correct answer is option 'C'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about An unknown polynomial yields a remainder of 2 upon division by x − 1, and a remainder of 1 upon division by x − 2. If this polynomial is divided by (x − 1)(x − 2), then the remainder isa)2b)3c)− x + 3d)x + 1Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An unknown polynomial yields a remainder of 2 upon division by x − 1, and a remainder of 1 upon division by x − 2. If this polynomial is divided by (x − 1)(x − 2), then the remainder isa)2b)3c)− x + 3d)x + 1Correct answer is option 'C'. Can you explain this answer?.
An unknown polynomial yields a remainder of 2 upon division by x − 1, and a remainder of 1 upon division by x − 2. If this polynomial is divided by (x − 1)(x − 2), then the remainder isa)2b)3c)− x + 3d)x + 1Correct answer is option 'C'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about An unknown polynomial yields a remainder of 2 upon division by x − 1, and a remainder of 1 upon division by x − 2. If this polynomial is divided by (x − 1)(x − 2), then the remainder isa)2b)3c)− x + 3d)x + 1Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An unknown polynomial yields a remainder of 2 upon division by x − 1, and a remainder of 1 upon division by x − 2. If this polynomial is divided by (x − 1)(x − 2), then the remainder isa)2b)3c)− x + 3d)x + 1Correct answer is option 'C'. Can you explain this answer?.
Solutions for An unknown polynomial yields a remainder of 2 upon division by x − 1, and a remainder of 1 upon division by x − 2. If this polynomial is divided by (x − 1)(x − 2), then the remainder isa)2b)3c)− x + 3d)x + 1Correct answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE.
Download more important topics, notes, lectures and mock test series for JEE Exam by signing up for free.
Here you can find the meaning of An unknown polynomial yields a remainder of 2 upon division by x − 1, and a remainder of 1 upon division by x − 2. If this polynomial is divided by (x − 1)(x − 2), then the remainder isa)2b)3c)− x + 3d)x + 1Correct answer is option 'C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
An unknown polynomial yields a remainder of 2 upon division by x − 1, and a remainder of 1 upon division by x − 2. If this polynomial is divided by (x − 1)(x − 2), then the remainder isa)2b)3c)− x + 3d)x + 1Correct answer is option 'C'. Can you explain this answer?, a detailed solution for An unknown polynomial yields a remainder of 2 upon division by x − 1, and a remainder of 1 upon division by x − 2. If this polynomial is divided by (x − 1)(x − 2), then the remainder isa)2b)3c)− x + 3d)x + 1Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of An unknown polynomial yields a remainder of 2 upon division by x − 1, and a remainder of 1 upon division by x − 2. If this polynomial is divided by (x − 1)(x − 2), then the remainder isa)2b)3c)− x + 3d)x + 1Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice An unknown polynomial yields a remainder of 2 upon division by x − 1, and a remainder of 1 upon division by x − 2. If this polynomial is divided by (x − 1)(x − 2), then the remainder isa)2b)3c)− x + 3d)x + 1Correct answer is option 'C'. Can you explain this answer? tests, examples and also practice JEE tests.
|
|
Explore Courses for JEE exam
|
|
Suggested Free Tests
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