Answer
The graph of f(x) does not intersect the x-axis.
Work Step by Step
Descartes's Rule of Signs (page 384)
Let $f(x)=a_{n}x^{n}+a_{n-1}x^{n-1}+\cdots+a_{2}x^{2}+a_{1}x+a_{0}$
be a polynomial with real coefficients.
1. The number of positive real zeros of $f$ is either
$\mathrm{a}$. the same as the number of sign changes of $f(x)$
or
$\mathrm{b}$. less than the number of sign changes of $f(x)$ by a positive even integer.
If $f(x)$ has only one variation in sign, then $f$ has exactly one positive real zero.
2. The number of NEGATIVE real zeros of $f$ is either
$\mathrm{a}$. the same as the number of sign changes of $f(-x)$
or
$\mathrm{b}$. less than the number of sign changes of $f(-x)$ by a positive even integer.
If $f(-x)$ has only one variation in sign, then $f$ has exactly one negative real zero.
-------------------------
We count the sign variations in
$f(x)=3x^{4}+5x^{4}+2$
and
$f(-x)=3(-x)^{4}+5(-x)^{2}+2=3x^{4}+5x^{4}+2$
1. No sign changes in $f(x)$ ... no positive real zeros
2. No sign changes in $f(-x)$ ... no negative real zeros
The graph of f(x) does not intersect the x-axis.
The screenshot of the graph confirms this (see image).
