Finding range of $m$ in $x^2+mx+6$. Find the range of values of $m$ in the quadratic equation $x^2+mx+6=0$ such that both the roots of the equation $\alpha,\beta<1$.
My attempt - it is given that
$\alpha<1$ and $\beta<1$
$\rightarrow \alpha+\beta<2$
But $\alpha+\beta=-m$
Thus $m>-2$.
But this solution doesn't involve the coefficient term i.e. $6$.
Any solution to the above question is appreciated.

This is a step-by-step description of how I would do it. There might be more clever ways out there, and there might be unanticipated problems with this approach, but it is the first thing I would try:


*

*Write an explicit formula for $\alpha$ and $\beta$ (it should use both the constant coefficient $6$ and the linear coefficient $m$)

*Decide which of $\alpha$ and $\beta$ is the biggest

*Set that root to be less than $1$

*Solve

