cmi-entrance 2022 Q8

cmi-entrance · India · pgmath 4 marks Complex numbers 2 Solving Polynomial Equations in C

Consider the complex polynomial $P ( x ) = x ^ { 6 } + i x ^ { 4 } + 1$. (Here $i$ denotes a square-root of $-1$.) Pick the correct statement(s) from below.
(A) $P$ has at least one real zero.
(B) $P$ has no real zeros.
(C) $P$ has at least three zeros of the form $\alpha + i \beta$ with $\beta < 0$.
(D) $P$ has exactly three zeros $\alpha + i \beta$ with $\beta > 0$.

Consider the complex polynomial $P ( x ) = x ^ { 6 } + i x ^ { 4 } + 1$. (Here $i$ denotes a square-root of $-1$.) Pick the correct statement(s) from below.\\
(A) $P$ has at least one real zero.\\
(B) $P$ has no real zeros.\\
(C) $P$ has at least three zeros of the form $\alpha + i \beta$ with $\beta < 0$.\\
(D) $P$ has exactly three zeros $\alpha + i \beta$ with $\beta > 0$.

Paper Questions

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