2 problems

Let $f$ be a polynomial of degree $4$ in $\mathbb{R}[\mathrm{x}_1,\mathrm{x}_2]$ and let $g$ be a polynomial of degree $2$ in $\mathbb{R}[\mathrm{x}_1,\mathrm{x}_2]$. Suppose there…

Let $f$ be a ternary quartic, that is, a $4$-form in $\mathbb{R}[\mathrm{x}_1,\mathrm{x}_2,\mathrm{x}_3]$, and let $g$ be a quadratic form in…