What is the nature of the roots of the equation \(x^2-9=0\)?

Correct answer: two real and distinct roots

Here, \(a=1\), \(b=0\), and \(c=-9\). The discriminant is \(D=b^2-4ac=0^2-4(1)(-9)=36>0\). Therefore, the roots are real and distinct; in fact, they are \(3\) and \(-3\). Equal roots require \(D=0\), so option B is incorrect. Exam tip: \(D>0\) indicates real and distinct roots, \(D=0\) indicates equal roots, and \(D<0\) indicates non-real roots.