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If the difference between the roots of the equation $x^{2} + a x + 1 = 0$ less then $\sqrt{5},$ then the set of possible value of a is

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(3,5)

(−∞,−3)

(−3,3)

(−3,∞)

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detailed solution

Correct option is C

Let α and β be the roots of the equation x2+ax+1=0then, α+β=−a and αβ=1 It is given that |α−β|<5⇒(α−β)2<5⇒ (α+β)2−4αβ<5⇒ a2−4<5⇒a2−9<0⇒−3

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If the difference between the roots of the equation x2+ax+1=0 less then 5, then the set of possible value of a is

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If the difference between the roots of the equation $x^{2} + a x + 1 = 0$ less then $\sqrt{5},$ then the set of possible value of a is