jee-advanced 2005 Q10

jee-advanced · India · screening Geometric Sequences and Series Nature of roots given coefficient constraints

10. Let $f ( x ) = a x ^ { 2 } + b x + c$, $a ^ { 1 } 0$ and $D = b ^ { 2 } - 4 a c$. If $a + b , a ^ { 2 } + b ^ { 2 }$ and $a ^ { 3 } + b ^ { 3 }$ are in G.P., then :
(a) $\quad \mathrm { D } ^ { 1 } 0$
(b) $\quad \mathrm { bD } ^ { 1 } 0$
(c) $\quad \mathrm { cD } ^ { 1 } 0$
(d) $\quad b c ^ { 1 } 0$

A plane at a distance of 1 unit from the origin cuts the coordinate axes at $A , B$ and $C$. If the centroid $D ( x , y , z )$ of the triangle $A B C$ satisfies the relation $\frac { 1 } { x ^ { 2 } } + \frac { 1 } { y ^ { 2 } } + \frac { 1 } { z ^ { 2 } } = k$, the value of $k$ is

10. Let $f ( x ) = a x ^ { 2 } + b x + c$, $a ^ { 1 } 0$ and $D = b ^ { 2 } - 4 a c$. If $a + b , a ^ { 2 } + b ^ { 2 }$ and $a ^ { 3 } + b ^ { 3 }$ are in G.P., then :\\
(a) $\quad \mathrm { D } ^ { 1 } 0$\\
(b) $\quad \mathrm { bD } ^ { 1 } 0$\\
(c) $\quad \mathrm { cD } ^ { 1 } 0$\\
(d) $\quad b c ^ { 1 } 0$\\

Paper Questions

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