A line has equation \(y=x-7\) and a curve has equation \(y=3x^2-5x+1\). Determine whether the line intersects, is a tangent to, or does not intersect the curve. Give a reason for your answer.[3]
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Answer:(a) \(x<-1\) or \(x>13\). (b) Does not intersect: discriminant \(-60<0\).