The number of real solutions of x^7 + 5x^3 + 3x + 1 = 0 is equal to ____________.

Question

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

Accepted Answer

$f^{\prime}(x)=7 x^{6}+15 x^{2}+3>0 \,\,\forall\,\, x \in R$

$f(x)$ is always increasing

So clearly it intersects

x-axis at only one point

Solutions · 1