The maximum possible number of real roots of | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Let $f(x) = x^5 - 6x^2 - 4x + 5$.For positive real roots,we check the sign changes in $f(x) = x^5 - 6x^2 - 4x + 5$. The signs are $(+, -, -, +)$.

Vedclass · Accepted Answer

$3$

Vedclass · Answer

(B) Let $f(x) = x^5 - 6x^2 - 4x + 5$.For positive real roots,we check the sign changes in $f(x) = x^5 - 6x^2 - 4x + 5$. The signs are $(+, -, -, +)$. There are $2$ sign changes.For negative real roots,we check the sign changes in $f(-x) = (-x)^5 - 6(-x)^2 - 4(-x) + 5 = -x^5 - 6x^2 + 4x + 5$. The signs are $(-, -, +, +)$. There is $1$ sign change.By Descartes' Rule of Signs,the maximum number of positive real roots is $2$ and the maximum number of negative real roots is $1$.Therefore,the maximum possible number of real roots is $2 + 1 = 3$.

The maximum possible number of real roots of the equation $x^5 - 6x^2 - 4x + 5 = 0$ is

Similar Questions

The anode mud in the electrolytic refining of silver contains

Which of the following is a characteristic of $Pteridophytes$?

Which of the following pairs represents biofertilizers?

Assertion $(A)$: The aqueous solution of $CH_3COONa$ is alkaline in nature. Reason $(R)$: Acetate ion undergoes anionic hydrolysis. The correct answer is

If $EAN$ of central metal cation $M^{2+}$ in a non-chelating complex is $36$ and atomic number of metal $M$ is $26$,then the number of monodentate ligands in this complex is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module