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The value of lambda such that sum of the...

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

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The correct Answer is:
2
We need to minimize `alpha^(2)+beta^(2)`
`alpha^(2)+beta^(2)=(alpha+beta)^(2)-2alpha beta`
`=lambda^(2)-6lambda+9+2lambda-4=lambda^(2)-4lambda+5`
Minimum value occurs at `lambda= -(b)/(2a)=(4)/(2)=2`
`lambda=2`
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