InterviewSolution
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InterviewSolution
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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 isA. `5/4`B. 1C. `15/8`D. 2 |
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Answer» 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.` |
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