1. **State the problem:** Find the values of $k$ such that the quadratic equation $$8x^2 + kx + 2 = 0$$ 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 roots are real if and only if $$\Delta \geq 0.$$ To have no real roots, we need $$\Delta < 0.$$ 3. **Identify coefficients:** Here, $a = 8$, $b = k$, and $c = 2$. 4. **Write the discriminant inequality:** $$ k^2 - 4 \times 8 \times 2 < 0 $$ 5. **Simplify:** $$ k^2 - 64 < 0 $$ 6. **Rewrite inequality:** $$ k^2 < 64 $$ 7. **Solve for $k$:** $$ -8 < k < 8 $$ **Final answer:** The quadratic equation has no real roots if and only if $$k$$ lies strictly between $$-8$$ and $$8$$.