isi-entrance 2018 Q28

isi-entrance · India · UGA Discriminant and conditions for roots Condition for repeated (equal/double) roots

For which values of $\theta$, with $0 < \theta < \pi / 2$, does the quadratic polynomial in $t$ given by $t ^ { 2 } + 4 t \cos \theta + \cot \theta$ have repeated roots?
(A) $\frac { \pi } { 6 }$ or $\frac { 5 \pi } { 18 }$
(B) $\frac { \pi } { 6 }$ or $\frac { 5 \pi } { 12 }$
(C) $\frac { \pi } { 12 }$ or $\frac { 5 \pi } { 18 }$
(D) $\frac { \pi } { 12 }$ or $\frac { 5 \pi } { 12 }$

For which values of $\theta$, with $0 < \theta < \pi / 2$, does the quadratic polynomial in $t$ given by $t ^ { 2 } + 4 t \cos \theta + \cot \theta$ have repeated roots?\\
(A) $\frac { \pi } { 6 }$ or $\frac { 5 \pi } { 18 }$\\
(B) $\frac { \pi } { 6 }$ or $\frac { 5 \pi } { 12 }$\\
(C) $\frac { \pi } { 12 }$ or $\frac { 5 \pi } { 18 }$\\
(D) $\frac { \pi } { 12 }$ or $\frac { 5 \pi } { 12 }$

Paper Questions

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