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If the difference between the roots of the equation x2 + ax + 1 = 0 is less than √5, then the set of possible values of a is
- a)(–3, –2] ∪ [2, 3)
- b)(–3, ∞)
- c)(3, ∞)
- d)(–∞, 3)
Correct answer is option 'A'. Can you explain this answer?
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The difference between the roots of a quadratic equation can be found using the discriminant. For the equation x^2 + ax + 1 = 0, the discriminant is given by b^2 - 4ac, where a = 1, b = a, and c = 1.
So, the discriminant is a^2 - 4(1)(1) = a^2 - 4.
If the difference between the roots is less than a, then the discriminant must be positive and less than a^2.
Therefore, a^2 - 4 > 0 and a^2 - 4 < a^2.="" />
Simplifying the inequalities, we have:
a^2 > 4 and -4 < 0.="" />
The first inequality, a^2 > 4, implies that a > 2 or a < -2.="" />
The second inequality, -4 < 0,="" is="" always="" true.="" />
So, the difference between the roots of the equation x^2 + ax + 1 = 0 is less than a if a > 2 or a < -2.="" />
So, the discriminant is a^2 - 4(1)(1) = a^2 - 4.
If the difference between the roots is less than a, then the discriminant must be positive and less than a^2.
Therefore, a^2 - 4 > 0 and a^2 - 4 < a^2.="" />
Simplifying the inequalities, we have:
a^2 > 4 and -4 < 0.="" />
The first inequality, a^2 > 4, implies that a > 2 or a < -2.="" />
The second inequality, -4 < 0,="" is="" always="" true.="" />
So, the difference between the roots of the equation x^2 + ax + 1 = 0 is less than a if a > 2 or a < -2.="" />
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If the difference between the roots of the equation x2+ ax + 1 = 0 is less than√5, then the set of possible values of a isa)(–3, –2] ∪ [2, 3)b)(–3, ∞)c)(3, ∞)d)(–∞, 3)Correct answer is option 'A'. Can you explain this answer?
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If the difference between the roots of the equation x2+ ax + 1 = 0 is less than√5, then the set of possible values of a isa)(–3, –2] ∪ [2, 3)b)(–3, ∞)c)(3, ∞)d)(–∞, 3)Correct answer is option 'A'. 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 the difference between the roots of the equation x2+ ax + 1 = 0 is less than√5, then the set of possible values of a isa)(–3, –2] ∪ [2, 3)b)(–3, ∞)c)(3, ∞)d)(–∞, 3)Correct answer is option 'A'. 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 the difference between the roots of the equation x2+ ax + 1 = 0 is less than√5, then the set of possible values of a isa)(–3, –2] ∪ [2, 3)b)(–3, ∞)c)(3, ∞)d)(–∞, 3)Correct answer is option 'A'. Can you explain this answer?.
If the difference between the roots of the equation x2+ ax + 1 = 0 is less than√5, then the set of possible values of a isa)(–3, –2] ∪ [2, 3)b)(–3, ∞)c)(3, ∞)d)(–∞, 3)Correct answer is option 'A'. 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 the difference between the roots of the equation x2+ ax + 1 = 0 is less than√5, then the set of possible values of a isa)(–3, –2] ∪ [2, 3)b)(–3, ∞)c)(3, ∞)d)(–∞, 3)Correct answer is option 'A'. 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 the difference between the roots of the equation x2+ ax + 1 = 0 is less than√5, then the set of possible values of a isa)(–3, –2] ∪ [2, 3)b)(–3, ∞)c)(3, ∞)d)(–∞, 3)Correct answer is option 'A'. Can you explain this answer?.
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If the difference between the roots of the equation x2+ ax + 1 = 0 is less than√5, then the set of possible values of a isa)(–3, –2] ∪ [2, 3)b)(–3, ∞)c)(3, ∞)d)(–∞, 3)Correct answer is option 'A'. Can you explain this answer?, a detailed solution for If the difference between the roots of the equation x2+ ax + 1 = 0 is less than√5, then the set of possible values of a isa)(–3, –2] ∪ [2, 3)b)(–3, ∞)c)(3, ∞)d)(–∞, 3)Correct answer is option 'A'. Can you explain this answer? has been provided alongside types of If the difference between the roots of the equation x2+ ax + 1 = 0 is less than√5, then the set of possible values of a isa)(–3, –2] ∪ [2, 3)b)(–3, ∞)c)(3, ∞)d)(–∞, 3)Correct answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
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