Number of Real Roots of a Higher-Order Polynomial

Consider the higher-order polynomial equation given by:

$$ f(x) = 4x^4 - 8x^3 + 6x^2 - 2 $$

To find the number of real solutions to the equation $$ f(x) = 0 $$, you can use the Rational Root Theorem and analyze the behavior of the function over the reals.

Determine the number of real roots of the equation.