If the difference between the roots of the eq | vedclass

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(D) Let the roots of the equation $x^2 + ax + 1 = 0$ be $\alpha$ and $\beta$.Given that the difference between the roots is $|\alpha - \beta| < \sqrt{

Vedclass · Accepted Answer

$(-3, -2) \cup (2, 3)$

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(D) Let the roots of the equation $x^2 + ax + 1 = 0$ be $\alpha$ and $\beta$.Given that the difference between the roots is $|\alpha - \beta| We know that $|\alpha - \beta| = \frac{\sqrt{D}}{|a_{coeff}|}$,where $D$ is the discriminant $b^2 - 4ac$.Here,$D = a^2 - 4(1)(1) = a^2 - 4$.Since the roots must be real for the difference to be defined in the real number system,we require $D \ge 0$,which means $a^2 \ge 4$,so $a \in (-\infty, -2] \cup [2, \infty)$.The condition $|\alpha - \beta| Squaring both sides,we get $a^2 - 4 This implies $-3 Combining the conditions $a \in (-\infty, -2] \cup [2, \infty)$ and $a \in (-3, 3)$,we get $a \in (-3, -2] \cup [2, 3)$.

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

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