Let P(x)=x10+a1 x9+a2 x8+ ldots ldots+a10 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

Question

Let P(x)=x10+a1 x9+a2 x8+ ldots ldots+a10 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

Tardigrade Admin · Accepted Answer

undersetx arrow-∞ textLim P(x) arrow ∞ text and undersetx arrow-∞ textLim P(x) arrow ∞ ∴ text Minimum number of zeros using I.V.T =4 .

Q. Let $P (x) = x^{10} + a_{1} x^{9} + a_{2} x^{8} + \dots\dots + a_{10}$ 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

5

4

3

2

$x \to - \infty Lim P (x) \to \infty and < b r / > x \to - \infty Lim P (x) \to \infty$
$∴ Minimum number of zeros using I.V.T = 4$ .

Q. Let P(x)=x10+a1​x9+a2​x8+……+a10​ 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

5

4

3

2

x→−∞Lim​P(x)→∞ and <br/>x→−∞Lim​P(x)→∞ ∴ Minimum number of zeros using I.V.T =4.

Q. Let $P (x) = x^{10} + a_{1} x^{9} + a_{2} x^{8} + \dots\dots + a_{10}$ 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

$x \to - \infty Lim P (x) \to \infty and < b r / > x \to - \infty Lim P (x) \to \infty$
$∴ Minimum number of zeros using I.V.T = 4$ .