jee-advanced 2003 Q14

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

14. If $f ( x ) = x ^ { 2 } + 2 b x + 2 c ^ { 2 }$ and $g ( x ) = - x ^ { 2 } - 2 c x + b ^ { 2 }$ such that min $f ( x ) > \max g ( x )$, then the relation between $b$ and $c$, is :
(a) no real value of $b$ and $c$
(b) $0 <$ c $<$ b $\sqrt { } 2$
(c) $| \mathrm { c } | < | \mathrm { b } | \sqrt { } 2$
(d) $| c | > | b | \sqrt { } 2$

If $n$ is a non-zero integer and

14. If $f ( x ) = x ^ { 2 } + 2 b x + 2 c ^ { 2 }$ and $g ( x ) = - x ^ { 2 } - 2 c x + b ^ { 2 }$ such that min $f ( x ) > \max g ( x )$, then the relation between $b$ and $c$, is :\\
(a) no real value of $b$ and $c$\\
(b) $0 <$ c $<$ b $\sqrt { } 2$\\
(c) $| \mathrm { c } | < | \mathrm { b } | \sqrt { } 2$\\
(d) $| c | > | b | \sqrt { } 2$\\

Paper Questions

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