What is the nature of the roots of \(2x^2-11x+15=0\)?

Correct answer: Two real, rational and distinct roots (\(\Delta=1\))

Here, \(a=2, b=-11, c=15\), so the discriminant is \(\Delta=b^2-4ac=(-11)^2-4(2)(15)=1\). Since \(\Delta\) is positive and a perfect square, the roots are real, rational, and distinct. In fact, \(2x^2-11x+15=(2x-5)(x-3)\), giving the roots \(x=\frac{5}{2}\) and \(x=3\). Exam tip: when \(\Delta>0\) and is a perfect square, the roots are rational and distinct.