• # question_answer 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) $2$

 ${{\alpha }^{2}}+{{\beta }^{2}}=(\alpha +{{\beta }^{2}})-2\alpha \beta$ $={{(3-\lambda )}^{2}}-2(2-\lambda )$ $={{\lambda }^{2}}+9-6\lambda -4+2\lambda$ $={{\lambda }^{2}}-4\lambda +5$ $\therefore$For least value$\lambda =2.$