What is the nature of the roots of the equation \(x^2-5x+6=0\)?

Correct answer: Two real and distinct

Here, \(a=1, b=-5, c=6\). The discriminant is \(D=b^2-4ac=(-5)^2-4(1)(6)=25-24=1\). Since \(D>0\), the quadratic equation has two real and distinct roots; in fact, the roots are \(2\) and \(3\). Remember: \(D>0\) gives real and distinct roots, \(D=0\) gives equal roots, and \(D<0\) gives no real roots.