Question

The value of ${}^{\prime }{a}^{\prime }$ for which the sum of the squares of the roots of $2x^2-2\left(a-2\right)x-a-1=0$ is least is -

• A. $1$
• B. $\frac{3}{2}$
• C. $2$
• D. $-1$

Answer 1

The correct option is B $\frac{3}{2}$

$2x^2-2(a-2)x-(a+1)=0$

Sum of squares of roots is $(a-2{)}^2+(a+1)=a^2-4a+4+a+1=a^2-3a+5=(a-\frac{3}{2}{)}^2+\frac{11}{4}$

This value will be least when $a=\frac{3}{2}$