A) (-3, 3)
B) \[\Delta S{}^\circ \]
C) \[\frac{1}{2}(1-\sqrt{5})\]
D) \[\frac{1}{2}\sqrt{5}\]
Correct Answer: A
Solution :
Let \[\alpha \] and \[\beta \] be the roots of equation \[{{x}^{2}}+ax+1=0,\]then \[\alpha +\beta =-a\] and \[\alpha \beta =1\] Now, \[|\alpha -\beta |=\sqrt{{{(\alpha +\beta )}^{2}}-4\alpha \beta }\] \[\Rightarrow \] \[|\alpha -\beta |=\sqrt{{{a}^{2}}-4}\] According to the question, \[\sqrt{{{a}^{2}}-4}<\sqrt{5}\Rightarrow {{a}^{2}}-4<5\] \[\Rightarrow \] \[{{a}^{2}}-9<0\Rightarrow a\in (-3,3)\]
You need to login to perform this action.
You will be redirected in
3 sec
