isi-entrance 2022 Q18

isi-entrance · India · UGA Roots of polynomials Existence or counting of roots with specified properties

Let $p$ and $q$ be two non-zero polynomials such that the degree of $p$ is less than or equal to the degree of $q$, and $p ( a ) q ( a ) = 0$ for $a = 0,1,2 , \ldots , 10$. Which of the following must be true?
(A) degree of $q \neq 10$
(B) degree of $p \neq 10$
(C) degree of $q \neq 5$
(D) degree of $p \neq 5$

Let $p$ and $q$ be two non-zero polynomials such that the degree of $p$ is less than or equal to the degree of $q$, and $p ( a ) q ( a ) = 0$ for $a = 0,1,2 , \ldots , 10$. Which of the following must be true?\\
(A) degree of $q \neq 10$\\
(B) degree of $p \neq 10$\\
(C) degree of $q \neq 5$\\
(D) degree of $p \neq 5$

Paper Questions

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