cmi-entrance 2011 QA7

cmi-entrance · India · ugmath 3 marks Factor & Remainder Theorem Divisibility and Factor Determination

When does the polynomial $1 + x + \cdots + x ^ { n }$ have $x - a$ as a factor? Here $n$ is a positive integer greater than 1000 and $a$ is a real number.
(A) if and only if $a = - 1$
(B) if and only if $a = - 1$ and $n$ is odd
(C) if and only if $a = - 1$ and $n$ is even
(D) We cannot decide unless $n$ is known.

When does the polynomial $1 + x + \cdots + x ^ { n }$ have $x - a$ as a factor? Here $n$ is a positive integer greater than 1000 and $a$ is a real number.\\
(A) if and only if $a = - 1$\\
(B) if and only if $a = - 1$ and $n$ is odd\\
(C) if and only if $a = - 1$ and $n$ is even\\
(D) We cannot decide unless $n$ is known.

Paper Questions

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