Question

If r and s are the roots of the equation x2 + bx + c = 0, where b and c are constants, is rs < 0 ? b < 0 c < 0

Answer 1

If
`r,s` are roots to the quadratic, then we can factor the quadratic and write


`(x-r)(x-s)=0=x^2-(r+s)x+rs`

so that
`-(r+s)=b` and
`rs=c`. It's not clear whether there's enough information given here, though... I'm guessing you're given that
`b<0` and
`c<0`, in which case you'd have
`rs>0`, so the answer would be no.