The equation of a curve is \(y=x^2-px+p^2+2\), where \(p\) is a constant. Determine the nature of roots of the equation for all real values of \(p\).[4]
Given that the curve \(y=(k+3)x^2+x-1\) has a minimum point and it intersects the line \(y=(k+1)x-2\) at 2 distinct points, find the range of values of \(k\).[4]
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Answer:(a) No real roots for every real \(p\). (b) \(-3<k<-2\) or \(k>6\).