Q of v vanishing makes the quadratic in alpha linear so there is one root not two

1. A.B(w, w) = 0
2. B.There exists an $\alpha \in \mathbb{R}$ such that $q(\alpha v+w)=0$.✓
3. C.There are infinitely many $\alpha \in \mathbb{R}$ such that $q(\alpha v+w)=0$.
4. D.q is equivalent to the quadratic form $Q(x,y)=x^2-y^2$ for all $(x,y)\in {\mathbb{R}}^2$.✓

The trap it tests

Boundary and endpoint

The statement turns at the edge of the interval, the domain, or the parameter range.