A) 0
B) 1
C) 2
D) 3
Correct Answer: C
Solution :
\[\alpha +\beta =\lambda -3\,\text{and }\alpha \beta =-\lambda \] \[{{\alpha }^{2}}+{{\beta }^{2}}={{(\alpha +\beta )}^{2}}-2\alpha \beta \] = \[{{(\lambda -3)}^{2}}+2\lambda \] = \[{{\lambda }^{2}}-4\lambda +9\] from options, for \[\lambda =0,\,{{({{\alpha }^{2}}+{{\beta }^{2}})}_{\lambda =0}}=9\] for \[\lambda =1,\,{{({{\alpha }^{2}}+{{\beta }^{2}})}_{\lambda =1}}=1-4+9=6\] for \[\lambda =2,\,{{({{\alpha }^{2}}+{{\beta }^{2}})}_{\lambda =2}}=4-8+9=5\] for \[\lambda =3,\,{{({{\alpha }^{2}}+{{\beta }^{2}})}_{\lambda =3}}=9-12+9=6\] \[{{\alpha }^{2}}+{{\beta }^{2}}\] is minimum for \[\lambda =2\].
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