The value of `lamda` such that sum of the squares of the roots of the quadratic equation, `x^(2)+(3-lamda)x+2=lamda` had the least value is
A. `5/4`
B. 1
C. `15/8`
D. 2
A. `5/4`
B. 1
C. `15/8`
D. 2
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Correct Answer – D
Given, quadratic equation is
`x^(2)+(3+ – lamda)x+2=lamda`
`x^(2)+(3-lamda)x+(2-lamda)=0″ “…(i)`
Let Eq. (1) has roots `alpha and beta,` then `alpha+beta,=lamda-3and alpha beta=2-lamda`
`” “”[“because”For” ax^(2)+bx+c=0, “sum of roots”=-b/a”and product of roots”=c/a”]”`
Now, `alpha^(2)+beta^(2)=(alpha+beta)^(2)-2alphabeta`
`=(lamda-3)^(2)-2(2-lamda)`
`=lamda^(2)-4lamda+5=(lamda^(2)-4lamda+4)+1=(lamda-2)^(2)+1`
Clearly, `almda^(2)+beta^(2)` will be least when `lamda=2.`