CAT Exam > CAT Questions > If the difference between the roots of the eq...
Start Learning for Free
If the difference between the roots of the equation x2 - 5x + 2k = 1 is 3, then find the value of k.
- a)2.2
- b)2.5
- c)4.2
- d)5.2
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
If the difference between the roots of the equation x2 - 5x + 2k = 1 i...
To find the value of k, we need to solve the given quadratic equation and determine the difference between its roots.
Given equation: x^2 - 5x + 2k = 1
Step 1: Rearrange the equation
x^2 - 5x + 2k - 1 = 0
Step 2: Use the quadratic formula to find the roots of the equation
The quadratic formula is given by:
x = (-b ± √(b^2 - 4ac)) / (2a)
Comparing the given equation with the general quadratic equation ax^2 + bx + c = 0, we have:
a = 1, b = -5, c = 2k - 1
Using the quadratic formula, we can find the roots of the equation.
Step 3: Calculate the discriminant
The discriminant, denoted as Δ, is given by Δ = b^2 - 4ac. It helps determine the nature of the roots.
In this case, we have:
Δ = (-5)^2 - 4(1)(2k - 1)
= 25 - 8k + 4
= 29 - 8k
Step 4: Find the roots
The roots of the equation can be found using the quadratic formula:
x = (-(-5) ± √(29 - 8k)) / (2(1))
= (5 ± √(29 - 8k)) / 2
Step 5: Calculate the difference between the roots
The difference between the roots is given by:
Difference = |(5 + √(29 - 8k)) / 2 - (5 - √(29 - 8k)) / 2|
= |√(29 - 8k) / 2 + √(29 - 8k) / 2|
= √(29 - 8k)
Step 6: Equate the difference to 3 and solve for k
√(29 - 8k) = 3
Squaring both sides of the equation, we get:
29 - 8k = 9
-8k = 9 - 29
-8k = -20
k = -20 / -8
k = 2.5
Therefore, the value of k is 2.5, which corresponds to option B.
Given equation: x^2 - 5x + 2k = 1
Step 1: Rearrange the equation
x^2 - 5x + 2k - 1 = 0
Step 2: Use the quadratic formula to find the roots of the equation
The quadratic formula is given by:
x = (-b ± √(b^2 - 4ac)) / (2a)
Comparing the given equation with the general quadratic equation ax^2 + bx + c = 0, we have:
a = 1, b = -5, c = 2k - 1
Using the quadratic formula, we can find the roots of the equation.
Step 3: Calculate the discriminant
The discriminant, denoted as Δ, is given by Δ = b^2 - 4ac. It helps determine the nature of the roots.
In this case, we have:
Δ = (-5)^2 - 4(1)(2k - 1)
= 25 - 8k + 4
= 29 - 8k
Step 4: Find the roots
The roots of the equation can be found using the quadratic formula:
x = (-(-5) ± √(29 - 8k)) / (2(1))
= (5 ± √(29 - 8k)) / 2
Step 5: Calculate the difference between the roots
The difference between the roots is given by:
Difference = |(5 + √(29 - 8k)) / 2 - (5 - √(29 - 8k)) / 2|
= |√(29 - 8k) / 2 + √(29 - 8k) / 2|
= √(29 - 8k)
Step 6: Equate the difference to 3 and solve for k
√(29 - 8k) = 3
Squaring both sides of the equation, we get:
29 - 8k = 9
-8k = 9 - 29
-8k = -20
k = -20 / -8
k = 2.5
Therefore, the value of k is 2.5, which corresponds to option B.
Free Test
FREE
| Start Free Test |
Community Answer
If the difference between the roots of the equation x2 - 5x + 2k = 1 i...
Let roots be a and b
equation be in the form ax2+bx+c=0
then the sum of roots=-b/a
product of roots =c/a
then sum of roots for this equation will be
a+b=-(-5)/1=5
product ab=2k
difference is given a-b=3
since we know (a-b)²=(a+b)²-4ab
(3)²=(5)²-4(2k-1)
9=25-8k+4
8k=20
k=2.5
equation be in the form ax2+bx+c=0
then the sum of roots=-b/a
product of roots =c/a
then sum of roots for this equation will be
a+b=-(-5)/1=5
product ab=2k
difference is given a-b=3
since we know (a-b)²=(a+b)²-4ab
(3)²=(5)²-4(2k-1)
9=25-8k+4
8k=20
k=2.5
|
Explore Courses for CAT exam
|
|
Similar CAT Doubts
Top Courses for CATView all
If the difference between the roots of the equation x2 - 5x + 2k = 1 is 3, then find the value of k.a)2.2b)2.5c)4.2d)5.2Correct answer is option 'B'. Can you explain this answer?
Question Description
If the difference between the roots of the equation x2 - 5x + 2k = 1 is 3, then find the value of k.a)2.2b)2.5c)4.2d)5.2Correct answer is option 'B'. Can you explain this answer? for CAT 2025 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about If the difference between the roots of the equation x2 - 5x + 2k = 1 is 3, then find the value of k.a)2.2b)2.5c)4.2d)5.2Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for CAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the difference between the roots of the equation x2 - 5x + 2k = 1 is 3, then find the value of k.a)2.2b)2.5c)4.2d)5.2Correct answer is option 'B'. Can you explain this answer?.
If the difference between the roots of the equation x2 - 5x + 2k = 1 is 3, then find the value of k.a)2.2b)2.5c)4.2d)5.2Correct answer is option 'B'. Can you explain this answer? for CAT 2025 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about If the difference between the roots of the equation x2 - 5x + 2k = 1 is 3, then find the value of k.a)2.2b)2.5c)4.2d)5.2Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for CAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the difference between the roots of the equation x2 - 5x + 2k = 1 is 3, then find the value of k.a)2.2b)2.5c)4.2d)5.2Correct answer is option 'B'. Can you explain this answer?.
Solutions for If the difference between the roots of the equation x2 - 5x + 2k = 1 is 3, then find the value of k.a)2.2b)2.5c)4.2d)5.2Correct answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for CAT.
Download more important topics, notes, lectures and mock test series for CAT Exam by signing up for free.
Here you can find the meaning of If the difference between the roots of the equation x2 - 5x + 2k = 1 is 3, then find the value of k.a)2.2b)2.5c)4.2d)5.2Correct answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
If the difference between the roots of the equation x2 - 5x + 2k = 1 is 3, then find the value of k.a)2.2b)2.5c)4.2d)5.2Correct answer is option 'B'. Can you explain this answer?, a detailed solution for If the difference between the roots of the equation x2 - 5x + 2k = 1 is 3, then find the value of k.a)2.2b)2.5c)4.2d)5.2Correct answer is option 'B'. Can you explain this answer? has been provided alongside types of If the difference between the roots of the equation x2 - 5x + 2k = 1 is 3, then find the value of k.a)2.2b)2.5c)4.2d)5.2Correct answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice If the difference between the roots of the equation x2 - 5x + 2k = 1 is 3, then find the value of k.a)2.2b)2.5c)4.2d)5.2Correct answer is option 'B'. Can you explain this answer? tests, examples and also practice CAT tests.
|
|
Explore Courses for CAT 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