Defence Exam > Defence Questions > A quadratic polynomial ax2+ bx + c = 0 is suc...
Start Learning for Free
A quadratic polynomial ax2 + bx + c = 0 is such that when it is divided by x, (x - 1) and (x + 1), the remainders are 3, 6 and 4 respectively. What is the value of (a + b)?
- a)3
- b)2
- c)1
- d)-1
Correct answer is option 'A'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
A quadratic polynomial ax2+ bx + c = 0 is such that when it is divided...
ax2 + bx + c = x (ax + b) + c
Remainder when divided by x = c
∴ c = 3
Remainder when divided by x = c
∴ c = 3
Let P(x) be a polynomial when divided by (x - a), then the remainder is P(a)
Remainder when divided by (x - 1) = P(1)
6 = a (1) + b(1) + c
6 = a + b + 3
∴ a + b = 3
6 = a (1) + b(1) + c
6 = a + b + 3
∴ a + b = 3
Most Upvoted Answer
A quadratic polynomial ax2+ bx + c = 0 is such that when it is divided...
Given information:
- Quadratic polynomial: ax^2 + bx + c = 0
- Remainders when divided by x, (x - 1), and (x + 1) are 3, 6, and 4 respectively
Calculating the Remainders:
- When the polynomial is divided by x, the remainder is 3
- This means that when x = 0, the polynomial evaluates to 3
- Hence, c = 3
- When the polynomial is divided by (x - 1), the remainder is 6
- This means that when x = 1, the polynomial evaluates to 6
- Substituting x = 1 in the polynomial, we get: a(1)^2 + b(1) + 3 = 6
- This simplifies to: a + b = 3
- When the polynomial is divided by (x + 1), the remainder is 4
- This means that when x = -1, the polynomial evaluates to 4
- Substituting x = -1 in the polynomial, we get: a(-1)^2 + b(-1) + 3 = 4
- This simplifies to: a - b = 1
Finding the Value of (a + b):
- Adding the equations a + b = 3 and a - b = 1, we get:
- 2a = 4
- a = 2
- Substituting the value of a in a + b = 3, we get:
- 2 + b = 3
- b = 1
- Therefore, the value of (a + b) = 2 + 1 = 3
Therefore, the correct answer is option A) 3.
|
Explore Courses for Defence exam
|
|
Similar Defence Doubts
A quadratic polynomial ax2+ bx + c = 0 is such that when it is divided by x, (x - 1) and (x + 1), the remainders are 3, 6 and 4 respectively. What is the value of (a + b)?a)3b)2c)1d)-1Correct answer is option 'A'. Can you explain this answer?
Question Description
A quadratic polynomial ax2+ bx + c = 0 is such that when it is divided by x, (x - 1) and (x + 1), the remainders are 3, 6 and 4 respectively. What is the value of (a + b)?a)3b)2c)1d)-1Correct answer is option 'A'. Can you explain this answer? for Defence 2024 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about A quadratic polynomial ax2+ bx + c = 0 is such that when it is divided by x, (x - 1) and (x + 1), the remainders are 3, 6 and 4 respectively. What is the value of (a + b)?a)3b)2c)1d)-1Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A quadratic polynomial ax2+ bx + c = 0 is such that when it is divided by x, (x - 1) and (x + 1), the remainders are 3, 6 and 4 respectively. What is the value of (a + b)?a)3b)2c)1d)-1Correct answer is option 'A'. Can you explain this answer?.
A quadratic polynomial ax2+ bx + c = 0 is such that when it is divided by x, (x - 1) and (x + 1), the remainders are 3, 6 and 4 respectively. What is the value of (a + b)?a)3b)2c)1d)-1Correct answer is option 'A'. Can you explain this answer? for Defence 2024 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about A quadratic polynomial ax2+ bx + c = 0 is such that when it is divided by x, (x - 1) and (x + 1), the remainders are 3, 6 and 4 respectively. What is the value of (a + b)?a)3b)2c)1d)-1Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A quadratic polynomial ax2+ bx + c = 0 is such that when it is divided by x, (x - 1) and (x + 1), the remainders are 3, 6 and 4 respectively. What is the value of (a + b)?a)3b)2c)1d)-1Correct answer is option 'A'. Can you explain this answer?.
Solutions for A quadratic polynomial ax2+ bx + c = 0 is such that when it is divided by x, (x - 1) and (x + 1), the remainders are 3, 6 and 4 respectively. What is the value of (a + b)?a)3b)2c)1d)-1Correct answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for Defence.
Download more important topics, notes, lectures and mock test series for Defence Exam by signing up for free.
Here you can find the meaning of A quadratic polynomial ax2+ bx + c = 0 is such that when it is divided by x, (x - 1) and (x + 1), the remainders are 3, 6 and 4 respectively. What is the value of (a + b)?a)3b)2c)1d)-1Correct answer is option 'A'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
A quadratic polynomial ax2+ bx + c = 0 is such that when it is divided by x, (x - 1) and (x + 1), the remainders are 3, 6 and 4 respectively. What is the value of (a + b)?a)3b)2c)1d)-1Correct answer is option 'A'. Can you explain this answer?, a detailed solution for A quadratic polynomial ax2+ bx + c = 0 is such that when it is divided by x, (x - 1) and (x + 1), the remainders are 3, 6 and 4 respectively. What is the value of (a + b)?a)3b)2c)1d)-1Correct answer is option 'A'. Can you explain this answer? has been provided alongside types of A quadratic polynomial ax2+ bx + c = 0 is such that when it is divided by x, (x - 1) and (x + 1), the remainders are 3, 6 and 4 respectively. What is the value of (a + b)?a)3b)2c)1d)-1Correct answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice A quadratic polynomial ax2+ bx + c = 0 is such that when it is divided by x, (x - 1) and (x + 1), the remainders are 3, 6 and 4 respectively. What is the value of (a + b)?a)3b)2c)1d)-1Correct answer is option 'A'. Can you explain this answer? tests, examples and also practice Defence tests.
|
|
Explore Courses for Defence 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