Question

The value of $\lambda$ such that sum of the squares of the roots of the quadratic equation, $x^2+(3-\lambda )x+2=\lambda$ has the least value is:

• A. $2$
• B. $\frac{4}{9}$
• C. $\frac{15}{8}$
• D. $1$

Answer 1

The correct option is A $2$

$\alpha +\beta =\lambda -3$

$\alpha \beta =2-\lambda$

${\alpha }^2+{\beta }^2=(\alpha +\beta {)}^2-2\alpha \beta =(\lambda -3{)}^2-2(2-\lambda )$

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

$={\lambda }^2-4\lambda +5$

$=(\lambda -2{)}^2+1$

$\therefore$ $\lambda =2$