Determine the product of all values of k for which the polynomial equation 2x^3 – 9x^2 + 12x – k = 0 has a double root. …Continue at the second page…

The tangent at point A (4, 16) to the curve defined by y = x^square root of x is extended to cut the x-axis at B and the y-axis at C. Determine the area of ΔOBC where O is the origin.