Condition for one root greater than k and the other less than k for JEE

Formula

\((k-\alpha)(k-\beta)<0\iff ak^2+bk+c\text{ has sign opposite to }a\)

Variables: \(\alpha,\beta\) are real roots, \(k\in\mathbb R\)

Conditions: \(a\neq 0\)

Location of roots relative to a number.