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Real and Non-Real Affine Intersection Points and Their Multiplicities

For the first 5 questions, consider the set of intersection points of two equations, and let a1 be the number of distinct affine real intersections with multiplicity one, let a2 be the number of distinct affine real intersections with multiplicity two, let b be the numberof distint complex non-real affine intersections and let c be the number of intersection points at infinity counting multiplicities. (for example, if there are two points at infinity or one point of multiplicity two at infinity, we will say in both cases that c = 2.)

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1. Answer: b)
, . So they are two parallel lines and intersect at infinity. Thus .
2. Answer: a)
, . Thus , then with multiplicity 2. . So the ...

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