3.19: Values of k for a tangent line to a curve

0606/21/M/J/21 — Question 7 · 6 marks

Find the exact values of the constant kk for which the line y=12x+1y = \dfrac{1}{2}x + 1 is a tangent to the curve y=4x2+kx+k2y = 4x^{2} + kx + k - 2.
[6]