Answer:
1/2
Explanation:
By Vieta's formulas, the sum of the roots of $ax^2 + bx + c$ is given by $\dfrac{-b}{a}$. For this quadratic, that value is
\[ \frac{-b}{a} = \frac{-(-4)}{4} = 1.\]
Since the sum of the roots is $1$, the average of the roots is $\boxed{\dfrac 1 2}$.
Alternately, we could factor $4$ out of every term of this quadratic, giving $4(x^2 - x - 1)$. Since $4 \cdot 0 = 0$, any number that is a root of $x^2 - x - 1$ will also be a root of $4(x^2 - x - 1)$. Thus, the problem can change to finding the sum of the roots of $x^2 - x - 1$.
Since the coefficient of the linear term is $-1$ and this is the opposite of the sum of the roots, we find that the sum of the roots is equal to $1$, and the average is $\boxed{\dfrac 1 2}$.