Question

Let $P(x)=x^{10}+a_1 x^9+a_2 x^8+\ldots \ldots+a_{10}$ be a polynomial with real coefficients. If $P(0)=1, P(1)$ $=1, P(2)=-1$, then minimum number of real zeros of $P(x)$ is equal to

• A. 5
• B. 4
• C. 3
• D. 2

Answer 1

Answer: (B)

$\underset{x \rightarrow-\infty}{ \text{Lim}} P(x) \rightarrow \infty \text { and }
\underset{x \rightarrow-\infty}{ \text{Lim}} P(x) \rightarrow \infty$
$\therefore \text { Minimum number of zeros using I.V.T }=4 $.