For the quadratic equation $x^2+px+q=0$, the sum of its roots is 5 and the product of its roots is -6. Find the values of $p$ and $q$.

Step-by-step solution

1. Let the roots be $r_1$ and $r_2$.
2. By Vieta’s formulas, $r_1+r_2=-p$ and $r_1{r}_2=q$.
3. Given $r_1+r_2=5$, we have $-p=5$ so $p=-5$.
4. Given $r_1{r}_2=-6$, we have $q=-6$.
5. Therefore $p=-5$ and $q=-6$.

Concept tested: Vieta's formulas for quadratic equations

Published 10 October 2026 · How this solution was prepared and checked