What is the discriminant of the following quadratic equation

[Yichen]

• quadratic equation ||v||^2 - c(2v·w)+c^2||w||^2=0, where c belongs to any real number, v and w are both vectors

 

[BvU]

Hello Yichen,

Please post in the homework forum. There is a most useful template there for questions like this.
If this is an equation, what are the knowns and what is the unknown ?
I read your equation as equivalent to $$\left ({\bf \vec v} - c {\bf \vec w } \right ) \cdot \left ({\bf \vec v} - c {\bf \vec w } \right ) = 0 $$ which certainly has a solution $\ {\bf \vec v} = c {\bf \vec w }$

 

[pasmith]

• quadratic equation ||v||^2 - c(2v·w)+c^2||w||^2=0, where c belongs to any real number, v and w are both vectors

Are you attempting to prove the Cauchy-Schwarz inequality?