Let $f(x,y)$ be a real bivariate polynomial. Suppose that $f(x,.)$
has no real roots when $x<0$, but has at least one real root when
$x>0$. Does it automatically follow that $f(0,.)$ has a double root ?
No, consider $f(x,y)=1-xy^2$. $ $
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10 months ago
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