If \(p\) is any real number, what will be the nature of the roots of the equation \(x^2+2px+p^2-1=0\)?

Correct answer: Always real and distinct

Here, \(a=1\), \(b=2p\), and \(c=p^2-1\). Therefore, the discriminant is \(D=b^2-4ac=(2p)^2-4(p^2-1)=4\). Since \(D>0\) for every real value of \(p\), both roots are always real and distinct. Option B is incorrect because equal roots require \(D=0\). Exam tip: For a quadratic involving a parameter, simplify the discriminant before testing particular parameter values.