If the difference between the roots of the eq | vedclass

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Question

(C) Let $\alpha$ and $\beta$ be the roots of the equation $x^2 + ax + 1 = 0$.From the properties of quadratic equations,we have $\alpha + \beta = -a$

Vedclass · Accepted Answer

$ (-3, 3) $

Vedclass · Answer

(C) Let $\alpha$ and $\beta$ be the roots of the equation $x^2 + ax + 1 = 0$.From the properties of quadratic equations,we have $\alpha + \beta = -a$ and $\alpha \beta = 1$.The difference between the roots is given by $|\alpha - \beta| = \sqrt{(\alpha + \beta)^2 - 4\alpha \beta}$.Substituting the values,we get $|\alpha - \beta| = \sqrt{(-a)^2 - 4(1)} = \sqrt{a^2 - 4}$.According to the given condition,$|\alpha - \beta| Therefore,$\sqrt{a^2 - 4} Squaring both sides,we get $a^2 - 4 This implies $|a| Thus,the set of possible values of $a$ is $a \in (-3, 3)$.

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

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