Tangent condition for line-curve

Find the parameter value for which a line is tangent to a curve, using the condition of equal roots (discriminant = 0).

1 questions · Standard +0.3

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CAIE P1 2018 November Q9
8 marks Standard +0.3
9 A curve has equation \(y = 2 x ^ { 2 } - 3 x + 1\) and a line has equation \(y = k x + k ^ { 2 }\), where \(k\) is a constant.
  1. Show that, for all values of \(k\), the curve and the line meet.
  2. State the value of \(k\) for which the line is a tangent to the curve and find the coordinates of the point where the line touches the curve.