1. **State the problem:** We need to find the values of $k$ for which the quadratic equation $$x^2 - kx + 4 = 0$$ has no real roots. 2. **Recall the discriminant condition:** For a quadratic equation $ax^2 + bx + c = 0$, the discriminant is $$\Delta = b^2 - 4ac.$$ The equation has no real roots if and only if $$\Delta < 0.$$ 3. **Identify coefficients:** Here, $a = 1$, $b = -k$, and $c = 4$. 4. **Write the discriminant inequality:** $$ \Delta = (-k)^2 - 4 \times 1 \times 4 < 0 $$ which simplifies to $$ k^2 - 16 < 0 $$ 5. **Solve the inequality:** $$ k^2 < 16 $$ Taking square roots, $$ -4 < k < 4 $$ 6. **Interpretation:** The quadratic has no real roots when $k$ is strictly between $-4$ and $4$. **Final answer:** $$ \boxed{-4 < k < 4} $$