JEE MAIN - Mathematics (2022 - 28th June Morning Shift - No. 10)

The number of real solutions of

$${x^7} + 5{x^3} + 3x + 1 = 0$$ is equal to ____________.
0
1
3
5

Explanation

JEE Main 2022 (Online) 28th June Morning Shift Mathematics - Application of Derivatives Question 82 English Explanation
$f^{\prime}(x)=7 x^{6}+15 x^{2}+3>0 \,\,\forall\,\, x \in R$

$f(x)$ is always increasing

So clearly it intersects

x-axis at only one point

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