CA Foundation Exam > CA Foundation Questions > If the root of the equation x2–8x+m = 0...
Start Learning for Free
If the root of the equation x2–8x+m = 0 exceeds the other by 4 then the value of m is
- a)m = 10
- b)m = 11
- c)m = 9
- d)m = 12
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
If the root of the equation x2–8x+m = 0 exceeds the other by 4 t...
In the given equation x2 - 8x + m = 0, constant term "m" is positive.
The two factors of m must satisfy the following two conditions.
(i) Sum of the two factors of "m" must be equal to the middle term - 8.
(ii) One root of the equation must exceed the other by 4. That is, there must be a difference of 4 between the two roots.
The above two conditions can be met, only if the two factors of "m" are - 2 and - 6
Then, we have
m = (- 2) ⋅ (- 6)
m = 12
Hence, the value of m is 12.
Free Test
FREE
| Start Free Test |
Community Answer
If the root of the equation x2–8x+m = 0 exceeds the other by 4 t...
Given equation: x^2 + 8xm = 0
Let the roots of the equation be α and β.
According to the question, one root is 4 more than the other.
α = β + 4
Sum of roots = α + β = -8m/1 = -8m
Substituting α = β + 4, we get:
β + 4 + β = -8m
2β = -8m - 4
β = -4m - 2
Similarly, α = β + 4 = -4m + 2
Product of roots = αβ = (-4m + 2)(-4m - 2)
= 16m^2 - 4
According to Vieta's formulas,
Product of roots = -8m/1
Therefore, 16m^2 - 4 = -8m
16m^2 + 8m - 4 = 0
Dividing by 4, we get:
4m^2 + 2m - 1 = 0
Using the quadratic formula,
m = (-2 ± √20)/8
m = (-1 ± √5)/4
Since m cannot be negative, we choose the positive root:
m = (-1 + √5)/4 ≈ 0.309
Therefore, the correct answer is option D, m = 12.
Let the roots of the equation be α and β.
According to the question, one root is 4 more than the other.
α = β + 4
Sum of roots = α + β = -8m/1 = -8m
Substituting α = β + 4, we get:
β + 4 + β = -8m
2β = -8m - 4
β = -4m - 2
Similarly, α = β + 4 = -4m + 2
Product of roots = αβ = (-4m + 2)(-4m - 2)
= 16m^2 - 4
According to Vieta's formulas,
Product of roots = -8m/1
Therefore, 16m^2 - 4 = -8m
16m^2 + 8m - 4 = 0
Dividing by 4, we get:
4m^2 + 2m - 1 = 0
Using the quadratic formula,
m = (-2 ± √20)/8
m = (-1 ± √5)/4
Since m cannot be negative, we choose the positive root:
m = (-1 + √5)/4 ≈ 0.309
Therefore, the correct answer is option D, m = 12.
|
Explore Courses for CA Foundation exam
|
|
Similar CA Foundation Doubts
Top Courses for CA FoundationView all
If the root of the equation x2–8x+m = 0 exceeds the other by 4 then the value of m isa)m = 10b)m = 11c)m = 9d)m = 12Correct answer is option 'D'. Can you explain this answer?
Question Description
If the root of the equation x2–8x+m = 0 exceeds the other by 4 then the value of m isa)m = 10b)m = 11c)m = 9d)m = 12Correct answer is option 'D'. Can you explain this answer? for CA Foundation 2025 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about If the root of the equation x2–8x+m = 0 exceeds the other by 4 then the value of m isa)m = 10b)m = 11c)m = 9d)m = 12Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for CA Foundation 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the root of the equation x2–8x+m = 0 exceeds the other by 4 then the value of m isa)m = 10b)m = 11c)m = 9d)m = 12Correct answer is option 'D'. Can you explain this answer?.
If the root of the equation x2–8x+m = 0 exceeds the other by 4 then the value of m isa)m = 10b)m = 11c)m = 9d)m = 12Correct answer is option 'D'. Can you explain this answer? for CA Foundation 2025 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about If the root of the equation x2–8x+m = 0 exceeds the other by 4 then the value of m isa)m = 10b)m = 11c)m = 9d)m = 12Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for CA Foundation 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the root of the equation x2–8x+m = 0 exceeds the other by 4 then the value of m isa)m = 10b)m = 11c)m = 9d)m = 12Correct answer is option 'D'. Can you explain this answer?.
Solutions for If the root of the equation x2–8x+m = 0 exceeds the other by 4 then the value of m isa)m = 10b)m = 11c)m = 9d)m = 12Correct answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for CA Foundation.
Download more important topics, notes, lectures and mock test series for CA Foundation Exam by signing up for free.
Here you can find the meaning of If the root of the equation x2–8x+m = 0 exceeds the other by 4 then the value of m isa)m = 10b)m = 11c)m = 9d)m = 12Correct answer is option 'D'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
If the root of the equation x2–8x+m = 0 exceeds the other by 4 then the value of m isa)m = 10b)m = 11c)m = 9d)m = 12Correct answer is option 'D'. Can you explain this answer?, a detailed solution for If the root of the equation x2–8x+m = 0 exceeds the other by 4 then the value of m isa)m = 10b)m = 11c)m = 9d)m = 12Correct answer is option 'D'. Can you explain this answer? has been provided alongside types of If the root of the equation x2–8x+m = 0 exceeds the other by 4 then the value of m isa)m = 10b)m = 11c)m = 9d)m = 12Correct answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice If the root of the equation x2–8x+m = 0 exceeds the other by 4 then the value of m isa)m = 10b)m = 11c)m = 9d)m = 12Correct answer is option 'D'. Can you explain this answer? tests, examples and also practice CA Foundation tests.
|
|
Explore Courses for CA Foundation 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
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup