Exercise 3.4.6 (Quadratic form whose discriminant is a perfect square)

Question

Let $d$ be a perfect square, possibly $0$. Show that there is a quadratic form $ax^2 + bxy + cy^2$ of discriminant $d$ for which $a = 0$

Richard Ganaye · Accepted Answer

\begin{proof} If $d$ is a perfect square, there is some inter $m$ such that $d = m^2$. Then the form
$$f(x,y) = mxy + y^2$$
has discriminant $m^2 = d$.
\end{proof}

Exercise 3.4.6 (Quadratic form whose discriminant is a perfect square)

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Exercise 3.4.6 (Quadratic form whose discriminant is a perfect square)

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