[Mailbag] What Do You Do with the Ideas You Used to Call “Mistakes”

Guillaume ParĂ©, in the very interesting comments of my last post where I
urged us to reconsider mistakes: I do agree with what is written, but I am
still w...
1 week ago
The answer is (6, 36).
ReplyDeleteThe equation of the circle has the form
x^2 + y^2 + ax + by + c = 0.
After substituting y = x^2, we have
x^2 + x^4 + ax + bx^2 + c = 0.
This is a fourthdegree equation, and the sum of the roots is zero, because the coefficient of x^3 is zero.
It is given that 1, 2, and 3 are roots. So the fourth root must be 6, and so the fourth point of intersection is (6, 36).