jee-main 2014 Q61

jee-main · India · 06apr Solving quadratics and applications Optimization or extremal value of an expression via completing the square

If $a \in R$ and the equation $- 3 ( x - [ x ] ) ^ { 2 } + 2 ( x - [ x ] ) + a ^ { 2 } = 0$ (where $[ x ]$ denotes the greatest integer $\leq x )$ has no integral solution, then all possible values of $a$ lie in the interval
(1) $( - 2 , - 1 )$
(2) $( - \infty , - 2 ) \cup ( 2 , \infty )$
(3) $( - 1,0 ) \cup ( 0,1 )$
(4) $( 1,2 )$

If $a \in R$ and the equation $- 3 ( x - [ x ] ) ^ { 2 } + 2 ( x - [ x ] ) + a ^ { 2 } = 0$ (where $[ x ]$ denotes the greatest integer $\leq x )$ has no integral solution, then all possible values of $a$ lie in the interval\\
(1) $( - 2 , - 1 )$\\
(2) $( - \infty , - 2 ) \cup ( 2 , \infty )$\\
(3) $( - 1,0 ) \cup ( 0,1 )$\\
(4) $( 1,2 )$

Paper Questions

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