jee-main 2020 Q51

jee-main · India · session2_03sep_shift2 Discriminant and conditions for roots Parameter range for specific root conditions (location/count)

The set of all real values of $\lambda$ for which the quadratic equation $\left( \lambda ^ { 2 } + 1 \right) x ^ { 2 } - 4 \lambda x + 2 = 0$ always have exactly one root in the interval $( 0,1 )$ is :
(1) $( - 3 , - 1 )$
(2) $( 0,2 )$
(3) $( 1,3 ]$
(4) $( 2,4 ]$

The set of all real values of $\lambda$ for which the quadratic equation $\left( \lambda ^ { 2 } + 1 \right) x ^ { 2 } - 4 \lambda x + 2 = 0$ always have exactly one root in the interval $( 0,1 )$ is :\\
(1) $( - 3 , - 1 )$\\
(2) $( 0,2 )$\\
(3) $( 1,3 ]$\\
(4) $( 2,4 ]$

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