If the quadratic equation \(x^2 + s x + 18 = 0\) has roots \(-3\) and \(-6\), what is the value of \(s\)?

9

For a quadratic \(ax^2+bx+c=0\), the sum of roots = \(-b/a\) and product = \(c/a\). Here \(a=1\) and \(b=s\), so the sum of roots is \(-s\). The given roots sum to \(-3)+(-6)=-9\), therefore \(-s=-9\) which gives \(s=9\). Common wrong answers: \(-9\) arises from forgetting the negative sign, \(18\) confuses sum with product (since product = 18), and \(-6\) mistakes a single root for the coefficient. Exam tip: identify \(a,b,c\) first and apply "sum = -b/a, product = c/a."

This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Introduction to Quadratic Equations.