Precalculus (6th Edition) Blitzer

$f$ cannot have any positive real zeroes and cannot have any negative real zeroes.
Consider a polynomial $f(x)=a_nx^n+a_{n-1} x^{n-1} +....+a_2 x^2+a_1x+a_0$ with real coefficients and $a_0 \ne 0$ Remember: 1) The number of positive real zeros of $f(x)$ is less than or equal to the number of variations in sign of $f(x)$. 2)The number of negative real zeros of $f(x)$ is less than or equal to the number of variations in sign of $f(-x)$. We see that $f(x)=f(-x)=2x^4+6x^2+8$ Thus, the function has no real roots.