Defence Exam > Defence Questions > If one root of5x2+13x+k=0 is reciprocal of th...
Start Learning for Free
If one root of 5x2+13x+k=0 is reciprocal of the other, then k is equal to
- a)5
- b)6
- c)1/6
- d)2
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
If one root of5x2+13x+k=0 is reciprocal of the other, then k is equal ...
let the two roots be a and 1/a
so product of roots
a x 1/a = k/5
k = 5
Most Upvoted Answer
If one root of5x2+13x+k=0 is reciprocal of the other, then k is equal ...
let the two roots be a and 1/a
so product of roots
a x 1/a = k/5
k = 5
Free Test
FREE
| Start Free Test |
Community Answer
If one root of5x2+13x+k=0 is reciprocal of the other, then k is equal ...
Explanation:
- Let the roots of the quadratic equation 5x^2 + 13x + k = 0 be a and 1/a (where a is not equal to 0).
- According to Vieta's formulas, the sum of the roots of a quadratic equation ax^2 + bx + c = 0 is -b/a and the product of the roots is c/a.
- In this case, the sum of the roots is a + 1/a = -13/5 and the product of the roots is k/5.
- Given that one root is the reciprocal of the other, we have a * 1/a = 1, which simplifies to a^2 = 1.
- Therefore, the roots are a = 1 and a = -1.
- Substituting these values into the sum of the roots equation gives us either 1 + 1 = -13/5 or -1 - 1 = -13/5.
- The first equation is not possible, so a = -1 is the root of the quadratic equation.
- Substituting a = -1 into the product of the roots equation gives us k/5 = -1, which implies k = -5.
- Therefore, the value of k is -5, which is equal to 5 when considering the absolute value, so the correct answer is option 'A'.
- Let the roots of the quadratic equation 5x^2 + 13x + k = 0 be a and 1/a (where a is not equal to 0).
- According to Vieta's formulas, the sum of the roots of a quadratic equation ax^2 + bx + c = 0 is -b/a and the product of the roots is c/a.
- In this case, the sum of the roots is a + 1/a = -13/5 and the product of the roots is k/5.
- Given that one root is the reciprocal of the other, we have a * 1/a = 1, which simplifies to a^2 = 1.
- Therefore, the roots are a = 1 and a = -1.
- Substituting these values into the sum of the roots equation gives us either 1 + 1 = -13/5 or -1 - 1 = -13/5.
- The first equation is not possible, so a = -1 is the root of the quadratic equation.
- Substituting a = -1 into the product of the roots equation gives us k/5 = -1, which implies k = -5.
- Therefore, the value of k is -5, which is equal to 5 when considering the absolute value, so the correct answer is option 'A'.
|
Explore Courses for Defence exam
|
|
If one root of5x2+13x+k=0 is reciprocal of the other, then k is equal toa)5b)6c)1/6d)2Correct answer is option 'A'. Can you explain this answer?
Question Description
If one root of5x2+13x+k=0 is reciprocal of the other, then k is equal toa)5b)6c)1/6d)2Correct answer is option 'A'. Can you explain this answer? for Defence 2025 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about If one root of5x2+13x+k=0 is reciprocal of the other, then k is equal toa)5b)6c)1/6d)2Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Defence 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If one root of5x2+13x+k=0 is reciprocal of the other, then k is equal toa)5b)6c)1/6d)2Correct answer is option 'A'. Can you explain this answer?.
If one root of5x2+13x+k=0 is reciprocal of the other, then k is equal toa)5b)6c)1/6d)2Correct answer is option 'A'. Can you explain this answer? for Defence 2025 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about If one root of5x2+13x+k=0 is reciprocal of the other, then k is equal toa)5b)6c)1/6d)2Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Defence 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If one root of5x2+13x+k=0 is reciprocal of the other, then k is equal toa)5b)6c)1/6d)2Correct answer is option 'A'. Can you explain this answer?.
Solutions for If one root of5x2+13x+k=0 is reciprocal of the other, then k is equal toa)5b)6c)1/6d)2Correct 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 one root of5x2+13x+k=0 is reciprocal of the other, then k is equal toa)5b)6c)1/6d)2Correct answer is option 'A'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
If one root of5x2+13x+k=0 is reciprocal of the other, then k is equal toa)5b)6c)1/6d)2Correct answer is option 'A'. Can you explain this answer?, a detailed solution for If one root of5x2+13x+k=0 is reciprocal of the other, then k is equal toa)5b)6c)1/6d)2Correct answer is option 'A'. Can you explain this answer? has been provided alongside types of If one root of5x2+13x+k=0 is reciprocal of the other, then k is equal toa)5b)6c)1/6d)2Correct answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice If one root of5x2+13x+k=0 is reciprocal of the other, then k is equal toa)5b)6c)1/6d)2Correct 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
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup