MCQ
Statement A (Assertion): The polynomial $p(x)=x^3+x$ has one real zero.
Statement R (Reason) : A polynomial of $n^{\text {th }}$ degree has at most $n-1$ zeroes.
  • A
    Both assertion (A) and reason ( $R$ ) are true and reason $(R)$ is the correct explanation of assertion $(A)$.
  • B
    Both assertion (A) and reason ( $R$ ) are true and reason $(R)$ is not the correct explanation of assertion (A).
  • Assertion $(A)$ is true but reason $(R)$ is false.
  • D
    Assertion (A) is false but reason $(R)$ is true.

Answer

Correct option: C.
Assertion $(A)$ is true but reason $(R)$ is false.
(c) : Clearly Reason is false.
We have, $p(x)=x^3+x=x\left(x^2+1\right)$
So, the value of $p(x)$ is zero when $x=0$ or $x^2+1=0$
But $x^2+1 \neq 0$ for any real value of $x \quad\left[\because x^2+1>0\right]$.
$\therefore \quad p(x)$ has one real zero, namely 0 .
So, Assertion is true.

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