Thank you Koopa, it is a trick appears in the topic of polynomials in pure mathematics syllabus, I did not used this method in the F.5 quiz as expected. Thank you again!

]]>Since x + 4y = 0 is the tangent to 3x + (y – 1)^3 = 4. We have 3(-4y) + (y – 1)^3 = 4 has a repeated root.

Hence we have: -12 + 3(y – 1)^2 = 0. Solving yields: y = 3 or -1.

However, y = 3 does not satisfy the original equation, therefore the repeated root is -1.

The rest is trivial.