If the roots of the quadratic equation $x^2-px+q=0$ are consecutive integers, find the value of $p^2-4q$.

Step 1: Let the roots of the quadratic equation be $\alpha$ and $\beta$. Since they are consecutive integers, we have:

Step 2: By Vieta's formulas, the sum and product of the roots are:

• $\alpha +\beta =p$

• $\alpha \beta =q$

Step 3: Express the squared difference in terms of the sum and product:

Step 4: Substitute the values from Vieta's formulas and step 1:

So the value of $p^2-4q$ is $1$. This is the discriminant of the quadratic equation.