Let $a_n, a_{n-1}, \ldots, a_1, a_0 \in \mathbb{C}$ and $f(x)=a_n x^n+a_{n-1} x^{n-1}+\ldots+$ $a_1 x+a_0$…

Let $a_n, a_{n-1}, \ldots, a_1, a_0 \in \mathbb{C}$ and $f(x)=a_n x^n+a_{n-1} x^{n-1}+\ldots+$ $a_1 x+a_0$ is a polynomial. If the polynomial $f(x)$ is monic then
  1. $a_n \neq 0$
  2. $a_n=1$
  3. $a_n>0$
  4. $\mathrm{a}_{\mathrm{n}} < 0$

Solution

We have $\mathrm{f}(\mathrm{x})=\mathrm{a}_{\mathrm{n}} \mathrm{x}^{\mathrm{n}}+\mathrm{a}_{\mathrm{n}-1} \times{ }^{\mathrm{n}-1}+\ldots . .+\mathrm{a}_1 \times \mathrm{a}_0$ here polynomial $f(x)$ is a monic polynomial should be 1 $ \Rightarrow \mathrm{a}_{\mathrm{n}}=1 $

Asked in: AP EAMCET 2022 (06 Jul Shift 1)

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