Which condition on \(k\) is required for the equation \(x^2-16x+k=0\) to have two real and distinct roots?

Correct answer: \(k<64\)

Here, \(a=1\), \(b=-16\), and \(c=k\). Thus, the discriminant is \(D=b^2-4ac=(-16)^2-4(1)(k)=256-4k\). Two real and distinct roots require \(D>0\), so \(256-4k>0\), which gives \(k<64\). When \(k=64\), the roots are equal, so that option is not correct. Exam tip: Check the sign of the discriminant first when determining the nature of roots.