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If both the roots of the quadratic equation x2 – 2kx + k2 + k – 5 = 0 are less than 5, then k lies in the interval
[AIEEE-2005]
- a)(5, 6]
- b)(6, ¥)
- c)(–¥, 4)
- d)[4, 5]
Correct answer is option 'C'. Can you explain this answer?
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If both the roots of the quadratic equation x2–2kx + k2+ k &ndas...
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If both the roots of the quadratic equation x2–2kx + k2+ k &ndas...
Understanding the given quadratic equation:
- The given quadratic equation is x^2 - 2kx + k^2 + k - 5 = 0.
- The roots of a quadratic equation are given by the formula (-b ± √(b^2 - 4ac)) / 2a.
Condition for roots less than 5:
- For both roots of the quadratic equation to be less than 5, the discriminant (b^2 - 4ac) should be greater than 0.
- In this case, the discriminant is (2k)^2 - 4(1)(k^2 + k - 5) = 4k^2 - 4k^2 - 16k + 20 = -16k + 20.
Solving for the discriminant:
- For the roots to be real and less than 5, the discriminant should be greater than 0.
- Therefore, we have -16k + 20 > 0.
- Solving this inequality, we get k < 20/16="" />
- So, the interval for k lies in (-∞, 5/4).
Identifying the correct option:
- The correct option among the given choices is option 'C' which represents the interval (-∞, 4).
- Therefore, the correct answer is option 'C' as k lies in the interval (-∞, 4) for the roots of the quadratic equation to be less than 5.
- The given quadratic equation is x^2 - 2kx + k^2 + k - 5 = 0.
- The roots of a quadratic equation are given by the formula (-b ± √(b^2 - 4ac)) / 2a.
Condition for roots less than 5:
- For both roots of the quadratic equation to be less than 5, the discriminant (b^2 - 4ac) should be greater than 0.
- In this case, the discriminant is (2k)^2 - 4(1)(k^2 + k - 5) = 4k^2 - 4k^2 - 16k + 20 = -16k + 20.
Solving for the discriminant:
- For the roots to be real and less than 5, the discriminant should be greater than 0.
- Therefore, we have -16k + 20 > 0.
- Solving this inequality, we get k < 20/16="" />
- So, the interval for k lies in (-∞, 5/4).
Identifying the correct option:
- The correct option among the given choices is option 'C' which represents the interval (-∞, 4).
- Therefore, the correct answer is option 'C' as k lies in the interval (-∞, 4) for the roots of the quadratic equation to be less than 5.
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If both the roots of the quadratic equation x2–2kx + k2+ k –5 = 0 are less than 5, then k lies in the interval[AIEEE-2005]a)(5, 6]b)(6, ¥)c)(–¥, 4)d)[4, 5]Correct answer is option 'C'. Can you explain this answer?
Question Description
If both the roots of the quadratic equation x2–2kx + k2+ k –5 = 0 are less than 5, then k lies in the interval[AIEEE-2005]a)(5, 6]b)(6, ¥)c)(–¥, 4)d)[4, 5]Correct answer is option 'C'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about If both the roots of the quadratic equation x2–2kx + k2+ k –5 = 0 are less than 5, then k lies in the interval[AIEEE-2005]a)(5, 6]b)(6, ¥)c)(–¥, 4)d)[4, 5]Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If both the roots of the quadratic equation x2–2kx + k2+ k –5 = 0 are less than 5, then k lies in the interval[AIEEE-2005]a)(5, 6]b)(6, ¥)c)(–¥, 4)d)[4, 5]Correct answer is option 'C'. Can you explain this answer?.
If both the roots of the quadratic equation x2–2kx + k2+ k –5 = 0 are less than 5, then k lies in the interval[AIEEE-2005]a)(5, 6]b)(6, ¥)c)(–¥, 4)d)[4, 5]Correct answer is option 'C'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about If both the roots of the quadratic equation x2–2kx + k2+ k –5 = 0 are less than 5, then k lies in the interval[AIEEE-2005]a)(5, 6]b)(6, ¥)c)(–¥, 4)d)[4, 5]Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If both the roots of the quadratic equation x2–2kx + k2+ k –5 = 0 are less than 5, then k lies in the interval[AIEEE-2005]a)(5, 6]b)(6, ¥)c)(–¥, 4)d)[4, 5]Correct answer is option 'C'. Can you explain this answer?.
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