If the roots of the quadratic equation \(x^2+px+4=0\) are real and distinct, which condition must \(p\) satisfy?

Correct answer: \(p^2>16\)

For \(x^2+px+4=0\), we have \(a=1\), \(b=p\), and \(c=4\). Real and distinct roots require the discriminant \(D=b^2-4ac\) to be positive. Thus, \(D=p^2-16>0\), which gives \(p^2>16\). If \(p^2=16\), the roots are equal, so option B is incorrect. Exam tip: remember that distinct real roots require \(D>0\).