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  4. The minimum value of the sum of the squares of the roots of x2+(3-a) x+1=2 a is:

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Q. The minimum value of the sum of the squares of the roots of $x^2+(3-a) x+1=2 a$ is:

JEE MainJEE Main 2022Complex Numbers and Quadratic Equations

Solution:

$\alpha^2+\beta^2=(\alpha+\beta)^2-2 \alpha \beta $
let $ f ( a )=(3- a )^2-2(1-2 a ) $
$f ( a )= a ^2-2 a +7 $
$f ( a )=( a -1)^2+6$ f
$( a ))_{\text {min. }}=6$