CAT Exam > CAT Questions > An equation 5005x 4 −bx 3 +cx 2 −...
Start Learning for Free
An equation 5005x 4 −bx 3 +cx 2 −dx+3774=0 has roots α, β, γ and δ and such that each of the roots is in the form of p/q where p and q are prime numbers. How many unordered quadruplets of roots α, β, γ, and δ are possible ?
- a)32
- b)24
- c)16
- d)12
Correct answer is option 'B'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Most Upvoted Answer
An equation 5005x 4 −bx 3 +cx 2 −dx+3774=0 has roots &alph...
We have 5005 = 5 x 7 x 11 x 13 and 3774 = 2 x 3 x 17 x 37
The product of roots for the given polynomial is given by =
Since, all the roots are of the for p/q where p,q ≠ 1 and both are prime.
∴ the roots should be such that the numerator must be one among 2, 3, 17 or 37 and the denominator must be one among 5, 7, 11 or 13.
Also, as each of the numbers is prime, so they will always be co-prime to each other.
For '2' as numerator we can select one of the denominators in 4 ways.
For '3' as numerator we can select one out of the remaining three denominators in 3 ways.
Similarly, For '17' as numerator we can select one out of the remaining two denominators in 2 ways.
And lastly for '37' as numerator we can select one out of the remaining one denominator in 1 way.
As all the selections are mutually dependent, so we have the total number of possible quadruplets as = 4 x 3 x 2 x 1 = 24
Hence, option B is the correct choice.
The product of roots for the given polynomial is given by =
Since, all the roots are of the for p/q where p,q ≠ 1 and both are prime.
∴ the roots should be such that the numerator must be one among 2, 3, 17 or 37 and the denominator must be one among 5, 7, 11 or 13.
Also, as each of the numbers is prime, so they will always be co-prime to each other.
For '2' as numerator we can select one of the denominators in 4 ways.
For '3' as numerator we can select one out of the remaining three denominators in 3 ways.
Similarly, For '17' as numerator we can select one out of the remaining two denominators in 2 ways.
And lastly for '37' as numerator we can select one out of the remaining one denominator in 1 way.
As all the selections are mutually dependent, so we have the total number of possible quadruplets as = 4 x 3 x 2 x 1 = 24
Hence, option B is the correct choice.
Attention CAT Students!
To make sure you are not studying endlessly, EduRev has designed CAT study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in CAT.
|
Explore Courses for CAT exam
|
|
Top Courses for CATView all
An equation 5005x 4 −bx 3 +cx 2 −dx+3774=0 has roots α, β, γ and δ and such that each of the roots is in the form of p/q where p and q are prime numbers. How many unordered quadruplets of roots α, β, γ, and δ are possible ?a)32b)24c)16d)12Correct answer is option 'B'. Can you explain this answer?
Question Description
An equation 5005x 4 −bx 3 +cx 2 −dx+3774=0 has roots α, β, γ and δ and such that each of the roots is in the form of p/q where p and q are prime numbers. How many unordered quadruplets of roots α, β, γ, and δ are possible ?a)32b)24c)16d)12Correct answer is option 'B'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about An equation 5005x 4 −bx 3 +cx 2 −dx+3774=0 has roots α, β, γ and δ and such that each of the roots is in the form of p/q where p and q are prime numbers. How many unordered quadruplets of roots α, β, γ, and δ are possible ?a)32b)24c)16d)12Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An equation 5005x 4 −bx 3 +cx 2 −dx+3774=0 has roots α, β, γ and δ and such that each of the roots is in the form of p/q where p and q are prime numbers. How many unordered quadruplets of roots α, β, γ, and δ are possible ?a)32b)24c)16d)12Correct answer is option 'B'. Can you explain this answer?.
An equation 5005x 4 −bx 3 +cx 2 −dx+3774=0 has roots α, β, γ and δ and such that each of the roots is in the form of p/q where p and q are prime numbers. How many unordered quadruplets of roots α, β, γ, and δ are possible ?a)32b)24c)16d)12Correct answer is option 'B'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about An equation 5005x 4 −bx 3 +cx 2 −dx+3774=0 has roots α, β, γ and δ and such that each of the roots is in the form of p/q where p and q are prime numbers. How many unordered quadruplets of roots α, β, γ, and δ are possible ?a)32b)24c)16d)12Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An equation 5005x 4 −bx 3 +cx 2 −dx+3774=0 has roots α, β, γ and δ and such that each of the roots is in the form of p/q where p and q are prime numbers. How many unordered quadruplets of roots α, β, γ, and δ are possible ?a)32b)24c)16d)12Correct answer is option 'B'. Can you explain this answer?.
Solutions for An equation 5005x 4 −bx 3 +cx 2 −dx+3774=0 has roots α, β, γ and δ and such that each of the roots is in the form of p/q where p and q are prime numbers. How many unordered quadruplets of roots α, β, γ, and δ are possible ?a)32b)24c)16d)12Correct 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 An equation 5005x 4 −bx 3 +cx 2 −dx+3774=0 has roots α, β, γ and δ and such that each of the roots is in the form of p/q where p and q are prime numbers. How many unordered quadruplets of roots α, β, γ, and δ are possible ?a)32b)24c)16d)12Correct answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
An equation 5005x 4 −bx 3 +cx 2 −dx+3774=0 has roots α, β, γ and δ and such that each of the roots is in the form of p/q where p and q are prime numbers. How many unordered quadruplets of roots α, β, γ, and δ are possible ?a)32b)24c)16d)12Correct answer is option 'B'. Can you explain this answer?, a detailed solution for An equation 5005x 4 −bx 3 +cx 2 −dx+3774=0 has roots α, β, γ and δ and such that each of the roots is in the form of p/q where p and q are prime numbers. How many unordered quadruplets of roots α, β, γ, and δ are possible ?a)32b)24c)16d)12Correct answer is option 'B'. Can you explain this answer? has been provided alongside types of An equation 5005x 4 −bx 3 +cx 2 −dx+3774=0 has roots α, β, γ and δ and such that each of the roots is in the form of p/q where p and q are prime numbers. How many unordered quadruplets of roots α, β, γ, and δ are possible ?a)32b)24c)16d)12Correct answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice An equation 5005x 4 −bx 3 +cx 2 −dx+3774=0 has roots α, β, γ and δ and such that each of the roots is in the form of p/q where p and q are prime numbers. How many unordered quadruplets of roots α, β, γ, and δ are possible ?a)32b)24c)16d)12Correct answer is option 'B'. Can you explain this answer? tests, examples and also practice CAT tests.
|
|
Explore Courses for CAT 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
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup