If the equation \(x^2-2px+p^2-5p=0\) has real and distinct roots, what is the correct condition on \(p\)?

Correct answer: \(p>0\)

For a quadratic equation to have real and distinct roots, its discriminant must satisfy \(D>0\). Here, \(a=1\), \(b=-2p\), and \(c=p^2-5p\), so \(D=b^2-4ac=4p^2-4(p^2-5p)=20p\). Thus, \(20p>0\), which gives \(p>0\). When \(p=0\), the discriminant is zero and the roots are equal, so \(p\ge0\) is not fully correct. Exam tip: For real and distinct roots, always use the condition \(D>0\).