How to find the roots of a 2 variable polynomial of 2nd degree?

Question

The following polynomial is just an example:

$$(3-3y)(x^2-y)$$

and is what does it mean to find the critical points of this polynomial? These are the maxima minima. Are they always concerned with my roots? For example:

$$3-3y=0$$ i know y=1 and now i plug it back to find my coordinate and now i have a point P(x,y). Similarly how do i do that with (x^2-y)=0, has Lagrange got anything to do with it. Please enlighten me with care and details! would love to know more about it.

Answer 1

See a similar post in Applying the Lagrangian function to find critical points.

If you want to learn about Lagrange multiplier, here is a good note: http://tutorial.math.lamar.edu/Classes/CalcIII/LagrangeMultipliers.aspx.