KVPY Sample Paper KVPY Stream-SX Model Paper-29

The value of K such that sum of the squares of the roots of quadratic equation,\[{{x}^{2}}+(3-\lambda )x+2=\lambda \] has the lest value is:

A) \[\frac{15}{8}\]

B) \[1\]

C) \[\frac{4}{9}\]

D) \[2\]

Correct Answer: D

Solution :

\[{{\alpha }^{2}}+{{\beta }^{2}}=(\alpha +{{\beta }^{2}})-2\alpha \beta \]

\[={{(3-\lambda )}^{2}}-2(2-\lambda )\]

\[={{\lambda }^{2}}+9-6\lambda -4+2\lambda \]

\[={{\lambda }^{2}}-4\lambda +5\]

\[\therefore \]For least value\[\lambda =2.\]