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  • The number of real solutions of <img alt="\mathrm{x^{7}+5x^{3}+3x+1= 0}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7Bx%5E%7B7%7D&plus;5x%5E%7B3%7D&plus;3x&plus;1%3D

The number of real solutions of \mathrm{x^{7}+5x^{3}+3x+1= 0} is equal to _________.

Option: 1

0


Option: 2

1


Option: 3

3


Option: 4

5


Answers (1)

best_answer

\mathrm{f\left ( x \right )= x^{7}+5x^{3}+3x+1}
\mathrm{{f}'\left ( x \right )= 7x^{6}+15x^{2}+3> 0\, \forall \, x\in R}

\mathrm{\Rightarrow f\left ( x \right )} is stictly increasing
\mathrm{\Rightarrow f\left ( x \right )}  will have exactly 1 real root .

Option (B)
 

Posted by

SANGALDEEP SINGH

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