cmi-entrance 2011 QA6

cmi-entrance · India · ugmath 3 marks Discriminant and conditions for roots Nature of roots given coefficient constraints

The equation $x ^ { 2 } + b x + c = 0$ has nonzero real coefficients satisfying $b ^ { 2 } > 4 c$. Moreover, exactly one of $b$ and $c$ is irrational. Consider the solutions $p$ and $q$ of this equation.
(A) Both $p$ and $q$ must be rational.
(B) Both $p$ and $q$ must be irrational.
(C) One of $p$ and $q$ is rational and the other irrational.
(D) We cannot conclude anything about rationality of $p$ and $q$ unless we know $b$ and $c$.

The equation $x ^ { 2 } + b x + c = 0$ has nonzero real coefficients satisfying $b ^ { 2 } > 4 c$. Moreover, exactly one of $b$ and $c$ is irrational. Consider the solutions $p$ and $q$ of this equation.\\
(A) Both $p$ and $q$ must be rational.\\
(B) Both $p$ and $q$ must be irrational.\\
(C) One of $p$ and $q$ is rational and the other irrational.\\
(D) We cannot conclude anything about rationality of $p$ and $q$ unless we know $b$ and $c$.

Paper Questions

QA1 QA2 QA3 QA4 QA5 QA6 QA7 QB1 QB2 QB3 QB4 QB5 QB6 QB7 QB8 QB9 QC1 QC2 QC3