1. **State the problem:** We need to find the values of $p$ such that the quadratic equation $2x^2 + px - 2p = 0$ has no real roots. 2. **Recall the condition for no real roots:** A quadratic equation $ax^2 + bx + c = 0$ has no real roots if its discriminant $\Delta$ is less than zero. 3. **Write the discriminant formula:** $$\Delta = b^2 - 4ac$$ 4. **Identify coefficients:** Here, $a = 2$, $b = p$, and $c = -2p$. 5. **Calculate the discriminant:** $$\Delta = p^2 - 4 \times 2 \times (-2p) = p^2 + 16p$$ 6. **Set the discriminant less than zero for no real roots:** $$p^2 + 16p < 0$$ 7. **Factor the inequality:** $$p(p + 16) < 0$$ 8. **Analyze the inequality:** The product $p(p + 16)$ is less than zero when one factor is positive and the other is negative. 9. **Determine intervals:** - If $p < 0$ and $p + 16 > 0$, then $-16 < p < 0$. 10. **Final answer:** The quadratic has no real roots if and only if $$-16 < p < 0$$