Location of Roots

If $(4a+c{)}^2<4b^2$ then one root of $a{x}^2+bx+c=0$ lies in

The value of $\lambda$ for which the equation $2x^2-2(2\lambda +1)x+\lambda (\lambda +1)=0$ may have one root less than $\lambda$ and other root greater than $\lambda$ are given by

If $1$ lies between the roots of the equation $3x^2-3\sin \alpha x-2{\cos }^2\alpha =0$ then $\alpha$ lies in the interval

For all $x\in R$ if $m{x}^2-9mx+5m+1>0,$ then $m$ lies in the interval

If both roots of the equation $x^2-2ax+a^2-1=0$ lies strictly between $-3$ and $4,$ then $\left[a\right]$ can be, where $[.]$ represents the greatest integer function