Defence Exam > Defence Questions > If (x + a) is a factor of both the quadratic ...
Start Learning for Free
If (x + a) is a factor of both the quadratic polynomials x2 + px + q and x2 + lx + m, where p, q, l and m are constants, then which one of the following is correct ?
- a)a = (m – q)/ (l – p) (l ≠ p)
- b)a = (m + q) / (l + p) (l ≠ p)
- c)l = (m – q) / (a – p) (a ≠ p)
- d)p = (m – q) / (a – l) (a ≠ l)
Correct answer is option 'A'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Most Upvoted Answer
If (x + a) is a factor of both the quadratic polynomials x2 + px + q a...
Explanation:
- Given: (x + a) is a factor of both x^2 + px + q and x^2 + lx + m
- Since (x + a) is a factor of x^2 + px + q, we have:
x^2 + px + q = (x + a)(x + k) where k is a constant
- Expanding the above equation, we get:
x^2 + px + q = x^2 + (a + k)x + ak
- Comparing coefficients of x in both equations, we get:
p = a + k and q = ak
- Since (x + a) is a factor of x^2 + lx + m, we have:
x^2 + lx + m = (x + a)(x + n) where n is a constant
- Expanding the above equation, we get:
x^2 + lx + m = x^2 + (a + n)x + an
- Comparing coefficients of x in both equations, we get:
l = a + n and m = an
- Solving the above equations simultaneously, we get:
a = (m - q)/(l - p)
Therefore, the correct answer is option 'A': a = (m - q)/(l - p).
- Given: (x + a) is a factor of both x^2 + px + q and x^2 + lx + m
- Since (x + a) is a factor of x^2 + px + q, we have:
x^2 + px + q = (x + a)(x + k) where k is a constant
- Expanding the above equation, we get:
x^2 + px + q = x^2 + (a + k)x + ak
- Comparing coefficients of x in both equations, we get:
p = a + k and q = ak
- Since (x + a) is a factor of x^2 + lx + m, we have:
x^2 + lx + m = (x + a)(x + n) where n is a constant
- Expanding the above equation, we get:
x^2 + lx + m = x^2 + (a + n)x + an
- Comparing coefficients of x in both equations, we get:
l = a + n and m = an
- Solving the above equations simultaneously, we get:
a = (m - q)/(l - p)
Therefore, the correct answer is option 'A': a = (m - q)/(l - p).
|
Explore Courses for Defence exam
|
|
Similar Defence Doubts
If (x + a) is a factor of both the quadratic polynomials x2 + px + q and x2 + lx + m, where p, q, l and m are constants, then which one of the following is correct ?a)a = (m q)/ (l p) (l p)b)a = (m + q) / (l + p) (l p)c)l = (m q) / (a p) (a p)d)p = (m q) / (a l) (a l)Correct answer is option 'A'. Can you explain this answer?
Question Description
If (x + a) is a factor of both the quadratic polynomials x2 + px + q and x2 + lx + m, where p, q, l and m are constants, then which one of the following is correct ?a)a = (m q)/ (l p) (l p)b)a = (m + q) / (l + p) (l p)c)l = (m q) / (a p) (a p)d)p = (m q) / (a l) (a l)Correct 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 If (x + a) is a factor of both the quadratic polynomials x2 + px + q and x2 + lx + m, where p, q, l and m are constants, then which one of the following is correct ?a)a = (m q)/ (l p) (l p)b)a = (m + q) / (l + p) (l p)c)l = (m q) / (a p) (a p)d)p = (m q) / (a l) (a l)Correct 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 If (x + a) is a factor of both the quadratic polynomials x2 + px + q and x2 + lx + m, where p, q, l and m are constants, then which one of the following is correct ?a)a = (m q)/ (l p) (l p)b)a = (m + q) / (l + p) (l p)c)l = (m q) / (a p) (a p)d)p = (m q) / (a l) (a l)Correct answer is option 'A'. Can you explain this answer?.
If (x + a) is a factor of both the quadratic polynomials x2 + px + q and x2 + lx + m, where p, q, l and m are constants, then which one of the following is correct ?a)a = (m q)/ (l p) (l p)b)a = (m + q) / (l + p) (l p)c)l = (m q) / (a p) (a p)d)p = (m q) / (a l) (a l)Correct 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 If (x + a) is a factor of both the quadratic polynomials x2 + px + q and x2 + lx + m, where p, q, l and m are constants, then which one of the following is correct ?a)a = (m q)/ (l p) (l p)b)a = (m + q) / (l + p) (l p)c)l = (m q) / (a p) (a p)d)p = (m q) / (a l) (a l)Correct 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 If (x + a) is a factor of both the quadratic polynomials x2 + px + q and x2 + lx + m, where p, q, l and m are constants, then which one of the following is correct ?a)a = (m q)/ (l p) (l p)b)a = (m + q) / (l + p) (l p)c)l = (m q) / (a p) (a p)d)p = (m q) / (a l) (a l)Correct answer is option 'A'. Can you explain this answer?.
Solutions for If (x + a) is a factor of both the quadratic polynomials x2 + px + q and x2 + lx + m, where p, q, l and m are constants, then which one of the following is correct ?a)a = (m q)/ (l p) (l p)b)a = (m + q) / (l + p) (l p)c)l = (m q) / (a p) (a p)d)p = (m q) / (a l) (a l)Correct 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 If (x + a) is a factor of both the quadratic polynomials x2 + px + q and x2 + lx + m, where p, q, l and m are constants, then which one of the following is correct ?a)a = (m q)/ (l p) (l p)b)a = (m + q) / (l + p) (l p)c)l = (m q) / (a p) (a p)d)p = (m q) / (a l) (a l)Correct answer is option 'A'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
If (x + a) is a factor of both the quadratic polynomials x2 + px + q and x2 + lx + m, where p, q, l and m are constants, then which one of the following is correct ?a)a = (m q)/ (l p) (l p)b)a = (m + q) / (l + p) (l p)c)l = (m q) / (a p) (a p)d)p = (m q) / (a l) (a l)Correct answer is option 'A'. Can you explain this answer?, a detailed solution for If (x + a) is a factor of both the quadratic polynomials x2 + px + q and x2 + lx + m, where p, q, l and m are constants, then which one of the following is correct ?a)a = (m q)/ (l p) (l p)b)a = (m + q) / (l + p) (l p)c)l = (m q) / (a p) (a p)d)p = (m q) / (a l) (a l)Correct answer is option 'A'. Can you explain this answer? has been provided alongside types of If (x + a) is a factor of both the quadratic polynomials x2 + px + q and x2 + lx + m, where p, q, l and m are constants, then which one of the following is correct ?a)a = (m q)/ (l p) (l p)b)a = (m + q) / (l + p) (l p)c)l = (m q) / (a p) (a p)d)p = (m q) / (a l) (a l)Correct answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice If (x + a) is a factor of both the quadratic polynomials x2 + px + q and x2 + lx + m, where p, q, l and m are constants, then which one of the following is correct ?a)a = (m q)/ (l p) (l p)b)a = (m + q) / (l + p) (l p)c)l = (m q) / (a p) (a p)d)p = (m q) / (a l) (a l)Correct 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