Solve the Problem $H$ Be the Set of All Polynomials of the Form

Solve the problem.
-Let $H$ be the set of all polynomials of the form $\mathrm { p } ( \mathrm { t } ) = \mathrm { a } + \mathrm { bt } ^ { 2 }$ where a and $\mathrm { b }$ are in $R$ and $b > a$ . Determine whether $\mathrm { H }$ is a vector space. If it is not a vector space, determine which of the following properties it fails to satisfy.
A: Contains zero vector
B: Closed under vector addition
C: Closed under multiplication by scalars

A) $\mathrm { H }$ is not a vector space; not closed under multiplication by scalars and does not contain zero vector
B) $\mathrm { H }$ is not a vector space; not closed under vector addition
C) $\mathrm { H }$ is not a vector space; not closed under multiplication by scalars
D) $\mathrm { H }$ is not a vector space; does not contain zero vector