If the difference between the roots of the equation x^2 + ax + 1 = 0 is less than √(5) , then the set of possible values of a is: - Mathematics MCQ AIEEE 2007 2026 | ExamTest.live

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If the difference between the roots of the equation x^{2} + a x + 1 = 0 is less than 5, then the set of possible values of a is:

Solution & Step-by-step Explanation

Let the roots be α and β . α + β = - a α β = 1 Difference ∣ α - β ∣ = (α + β)^{2} - 4 α β = a^{2} - 4 .Given ∣ α - β ∣ < 5 : a^{2} - 4 < 5 Squaring both sides (noting that a^{2} - 4 \geq 0 for real roots): a^{2} - 4 < 5 a^{2} < 9 ⟹ - 3 < a < 3 Thus, a \in (- 3, 3) .

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If the difference between the roots of the equation x^{2} + a x + 1 = 0 is less than 5, then the set of possible values of a is:

(- 3, 3)

(- 3, \infty)

(3, \infty)

(- \infty, - 3)

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