A) 1
B) 2
C) \[\frac{15}{8}\]
D) \[\frac{4}{9}\]
Correct Answer: B
Solution :
Sum of roots \[\alpha +\beta =-(3-\lambda )\] Product of roots \[\alpha \beta \,\,=\,\,2-\lambda \] \[{{\alpha }^{2}}+{{\beta }^{2}}={{\left( \alpha +\beta \right)}^{2}}-2\alpha \beta \] \[=\,\,{{(3-\lambda )}^{2}}-2(2-\lambda )\] \[=\text{ }9+{{\lambda }^{2}}-6\lambda -4+2\lambda \] \[=\,\,{{\lambda }^{2}}-4\,\lambda +5\] \[{{\alpha }^{2}}+{{\beta }^{2}}\] is least then \[\lambda =-\frac{b}{2a}\] \[\lambda =-\frac{-(-4)}{2}\,\,=\,\,2\]
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