The curve is given by $y = 4x^2 - kx + \frac{1}{2}k^2$ and the line is given by $y = x - a$, where $k$ and $a$ are constants.
(a)[4]
Knowing that the curve and the line intersect at the points with $x$-coordinates $0$ and $\frac{3}{4}$, find the values of $k$ and $a$.
(b)[5]
Given instead that $a = -\frac{7}{2}$, find the values of $k$ for which the line is a tangent to the curve.
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This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Sets the curve equal to the line at $x=0$.” …
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