CAT Exam > CAT Questions > Given the quadratic equation x2- (A - 3)x - (...
Start Learning for Free
Given the quadratic equation x2 - (A - 3)x - (A - 7), for what value of A will the sum of the squares of the roots be zero?
- a)- 2
- b)3
- c)6
- d)None of these
Correct answer is option 'D'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Most Upvoted Answer
Given the quadratic equation x2- (A - 3)x - (A - 7), for what value of...
Let the roots be p and q.
The given quadratic equation can be written as ax2 + bx + c, where a = 1, b = - (A - 3), c = - (A - 7).
The sum of the roots is (p + q) = (-b/a) = (A - 3), and the product of the roots is (pq) = (c/a) = (- A + 7).
The sum of the squares of the roots is [(p + q)2 - 2pq ] = (A - 3)2 - 2(-A + 7) = 0.
Solving this quadratic, we get A = 5 or A = -1.
Neither of these values is among the first three choices.
The given quadratic equation can be written as ax2 + bx + c, where a = 1, b = - (A - 3), c = - (A - 7).
The sum of the roots is (p + q) = (-b/a) = (A - 3), and the product of the roots is (pq) = (c/a) = (- A + 7).
The sum of the squares of the roots is [(p + q)2 - 2pq ] = (A - 3)2 - 2(-A + 7) = 0.
Solving this quadratic, we get A = 5 or A = -1.
Neither of these values is among the first three choices.
Community Answer
Given the quadratic equation x2- (A - 3)x - (A - 7), for what value of...
The given quadratic equation is x^2 - (A - 3)x - (A - 7) = 0.
To find the sum of the squares of the roots, we need to find the roots of the quadratic equation and then calculate their squares.
Let's solve the quadratic equation using the quadratic formula: x = (-b ± √(b^2 - 4ac)) / (2a).
Comparing the given equation with the standard form ax^2 + bx + c = 0, we have:
a = 1
b = -(A - 3)
c = -(A - 7)
Now, substituting the values of a, b, and c into the quadratic formula, we get:
x = (A - 3 ± √((A - 3)^2 - 4(1)(-(A - 7)))) / (2(1))
x = (A - 3 ± √(A^2 - 6A + 9 + 4A - 28)) / 2
x = (A - 3 ± √(A^2 - 2A - 19)) / 2
The roots of the quadratic equation are given by x1 and x2, where:
x1 = (A - 3 + √(A^2 - 2A - 19)) / 2
x2 = (A - 3 - √(A^2 - 2A - 19)) / 2
To find the sum of the squares of the roots, we calculate (x1)^2 + (x2)^2.
(x1)^2 + (x2)^2 = [(A - 3 + √(A^2 - 2A - 19)) / 2]^2 + [(A - 3 - √(A^2 - 2A - 19)) / 2]^2
Expanding and simplifying the above expression, we get:
(x1)^2 + (x2)^2 = (A^2 - 6A + 9 + 2(A - 3)√(A^2 - 2A - 19) + A^2 - 6A + 9 + 2(A - 3)√(A^2 - 2A - 19)) / 4
(x1)^2 + (x2)^2 = (2A^2 - 12A + 18 + 4(A - 3)√(A^2 - 2A - 19)) / 4
(x1)^2 + (x2)^2 = (A^2 - 6A + 9 + 2(A - 3)√(A^2 - 2A - 19)) / 2
For the sum of the squares of the roots to be zero, we need:
(A^2 - 6A + 9 + 2(A - 3)√(A^2 - 2A - 19)) / 2 = 0
A^2 - 6A + 9 + 2(A - 3)√(A^2 - 2A - 19) = 0
Simplifying the above equation:
A^2 - 6A +
To find the sum of the squares of the roots, we need to find the roots of the quadratic equation and then calculate their squares.
Let's solve the quadratic equation using the quadratic formula: x = (-b ± √(b^2 - 4ac)) / (2a).
Comparing the given equation with the standard form ax^2 + bx + c = 0, we have:
a = 1
b = -(A - 3)
c = -(A - 7)
Now, substituting the values of a, b, and c into the quadratic formula, we get:
x = (A - 3 ± √((A - 3)^2 - 4(1)(-(A - 7)))) / (2(1))
x = (A - 3 ± √(A^2 - 6A + 9 + 4A - 28)) / 2
x = (A - 3 ± √(A^2 - 2A - 19)) / 2
The roots of the quadratic equation are given by x1 and x2, where:
x1 = (A - 3 + √(A^2 - 2A - 19)) / 2
x2 = (A - 3 - √(A^2 - 2A - 19)) / 2
To find the sum of the squares of the roots, we calculate (x1)^2 + (x2)^2.
(x1)^2 + (x2)^2 = [(A - 3 + √(A^2 - 2A - 19)) / 2]^2 + [(A - 3 - √(A^2 - 2A - 19)) / 2]^2
Expanding and simplifying the above expression, we get:
(x1)^2 + (x2)^2 = (A^2 - 6A + 9 + 2(A - 3)√(A^2 - 2A - 19) + A^2 - 6A + 9 + 2(A - 3)√(A^2 - 2A - 19)) / 4
(x1)^2 + (x2)^2 = (2A^2 - 12A + 18 + 4(A - 3)√(A^2 - 2A - 19)) / 4
(x1)^2 + (x2)^2 = (A^2 - 6A + 9 + 2(A - 3)√(A^2 - 2A - 19)) / 2
For the sum of the squares of the roots to be zero, we need:
(A^2 - 6A + 9 + 2(A - 3)√(A^2 - 2A - 19)) / 2 = 0
A^2 - 6A + 9 + 2(A - 3)√(A^2 - 2A - 19) = 0
Simplifying the above equation:
A^2 - 6A +
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
|
|
Similar CAT Doubts
Top Courses for CATView all
Given the quadratic equation x2- (A - 3)x - (A - 7), for what value of A will the sum of the squares of the roots be zero?a)- 2b)3c)6d)None of theseCorrect answer is option 'D'. Can you explain this answer?
Question Description
Given the quadratic equation x2- (A - 3)x - (A - 7), for what value of A will the sum of the squares of the roots be zero?a)- 2b)3c)6d)None of theseCorrect answer is option 'D'. 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 Given the quadratic equation x2- (A - 3)x - (A - 7), for what value of A will the sum of the squares of the roots be zero?a)- 2b)3c)6d)None of theseCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Given the quadratic equation x2- (A - 3)x - (A - 7), for what value of A will the sum of the squares of the roots be zero?a)- 2b)3c)6d)None of theseCorrect answer is option 'D'. Can you explain this answer?.
Given the quadratic equation x2- (A - 3)x - (A - 7), for what value of A will the sum of the squares of the roots be zero?a)- 2b)3c)6d)None of theseCorrect answer is option 'D'. 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 Given the quadratic equation x2- (A - 3)x - (A - 7), for what value of A will the sum of the squares of the roots be zero?a)- 2b)3c)6d)None of theseCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Given the quadratic equation x2- (A - 3)x - (A - 7), for what value of A will the sum of the squares of the roots be zero?a)- 2b)3c)6d)None of theseCorrect answer is option 'D'. Can you explain this answer?.
Solutions for Given the quadratic equation x2- (A - 3)x - (A - 7), for what value of A will the sum of the squares of the roots be zero?a)- 2b)3c)6d)None of theseCorrect answer is option 'D'. 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 Given the quadratic equation x2- (A - 3)x - (A - 7), for what value of A will the sum of the squares of the roots be zero?a)- 2b)3c)6d)None of theseCorrect answer is option 'D'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
Given the quadratic equation x2- (A - 3)x - (A - 7), for what value of A will the sum of the squares of the roots be zero?a)- 2b)3c)6d)None of theseCorrect answer is option 'D'. Can you explain this answer?, a detailed solution for Given the quadratic equation x2- (A - 3)x - (A - 7), for what value of A will the sum of the squares of the roots be zero?a)- 2b)3c)6d)None of theseCorrect answer is option 'D'. Can you explain this answer? has been provided alongside types of Given the quadratic equation x2- (A - 3)x - (A - 7), for what value of A will the sum of the squares of the roots be zero?a)- 2b)3c)6d)None of theseCorrect answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Given the quadratic equation x2- (A - 3)x - (A - 7), for what value of A will the sum of the squares of the roots be zero?a)- 2b)3c)6d)None of theseCorrect answer is option 'D'. 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
|
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