If the roots of the equation \(x^2+px+6=0\) are real and distinct, which of the following conditions on \(p\) is correct?

Correct answer: \(p^2>24\)

For a quadratic equation \(ax^2+bx+c=0\), the roots are real and distinct when the discriminant \(D=b^2-4ac\) is positive. Here, \(a=1\), \(b=p\), and \(c=6\), so \(D=p^2-24\). Therefore, \(p^2-24>0\), which gives \(p^2>24\). If \(p^2=24\), the roots are real but equal. Exam tip: remember that real and distinct roots require \(D>0\).