Exams Joint Entrance Examination Mathematics Quadratic Equations and Inequalities Question 107 Question 107 of 157 Medium MCQ
The value of \[\lambda \] such that sum of the squares of the roots of the quadratic equation, x2 + (3 -- \[\lambda \])x + 2 = \[\lambda \] has the least value is -
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\[\alpha \] + \[\beta \] = \[\lambda \] - 3
\[\alpha \] β \beta β = 2 − - − λ \lambda λ α \alpha α 2 + β \beta β 2 = ( α \alpha α + β \beta β )2 − - − 2 α \[ \alpha \[ α \[ \beta \] = (\[\lambda \] - 3)2 - 2\[\left( {2 - \lambda } \right)\]
= \[\lambda \]2 + 9 - 6\[\lambda \] - 4 + 2\[\lambda \]
= \[\lambda \]2 - 4\[\lambda \] + 5
= (\[\lambda \] - 2)2 + 1
\[ \therefore \] \[\lambda \] = 2 Answer the question to unlock