The answer that the quadratic should have exactly one positive root should be correct.

I think you agree that the quadratic always has two real roots, so let's focus on Vieta's theorem for $x^2+px+q=0$. By Vieta's theorem:

• The sum of the roots is $-p$.
• The product of the roots is $q$.

Thus, if we know that $p$ is positive, then the sum of the roots is negative, and if $q$ is negative, then the product of the roots is negative. This is only possible if one root is positive and one root is negative.

If it helps, you can visualize the graph using Desmos and check different values of $p$ and $q$ here: www.desmos.com/calculator/e0gxboxui6

Hope this helps! Let us know if you have any further questions.