Exams Joint Entrance Examination Mathematics Quadratic Equations and Inequalities Question 111 Question 111 of 157 Medium MCQ
If \[\lambda \] be the ratio of the roots of the quadratic equation in x, 3m2x2 + m(m -- 4)x + 2 = 0, then the least value of m for which \[\lambda + {1 \over \lambda } = 1,\] is
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3m2x2 + m(m - 4) x + 2 = 0
\[\lambda + {1 \over \lambda } = 1,{\alpha \over \beta } + {\beta \over \alpha } = 1,{\alpha ^2} + {\beta ^2} = \alpha \beta \]
(\[\alpha \] + \[\beta \])2 = 3\[\alpha \] β \beta β ( − m ( m − 4 ) 3 m 2 ) 2 = 3 ( 2 ) 3 m 2 , ( m − 4 ) 2 9 m 2 = 6 3 m {\left( { - {{m\left( {m - 4} \right)} \over {3{m^2}}}} \right)^2} = {{3\left( 2 \right)} \over {3{m^2}}},{{{{\left( {m - 4} \right)}^2}} \over {9{m^2}}} = {6 \over {3m}} ( − 3 m 2 m ( m − 4 ) ) 2 = 3 m 2 3 ( 2 ) , 9 m 2 ( m − 4 ) 2 = 3 m 6 ( m − 4 ) 2 = 18 , m = 4 ± 18 , 4 ± 3 2 {\left( {m - 4} \right)^2} = 18,m = 4 \pm \sqrt {18,} \,\,4 \pm 3\sqrt 2 ( m − 4 ) 2 = 18 , m = 4 ± 18 , 4 ± 3 2 Answer the question to unlock