An area-based problem leads to the equation \(s^2-6s+10=0\). What is the correct conclusion about the real values of \(s\)?

Correct answer: No real roots \((D<0)\)

For the quadratic equation, \(a=1\), \(b=-6\), and \(c=10\). Thus, the discriminant is \(D=b^2-4ac=(-6)^2-4(1)(10)=36-40=-4\). Since \(D<0\), the equation has no real roots, so \(s\) cannot have a real value in the area problem. Exam tip: \(D<0\), \(D=0\), and \(D>0\) indicate no real roots, equal real roots, and distinct real roots, respectively.