GATE Electrical Engineering (EE) 2021 Solved Papers

Number of real $\left(+\mathit{v}\mathit{e}\right)$ roots $\le$ Number of sign changes in $\mathit{p}\left(\mathit{x}\right)=2$
Number of real $\left(-\mathit{v}\mathit{e}\right)$ rots $\le$ Number of sign changes in $\mathit{p}\left(-\mathit{x}\right)=0$
So, $\mathit{p}\left(\mathit{x}\right)=0$ has no $\left(-\mathit{v}\mathit{e}\right)$ real roots and a maximum of $2\left(+\mathit{v}\mathit{e}\right)$ real roots
$\therefore$ Number of real roots of ' $\mathit{P}\left(\mathit{x}\right)=0^{\prime }\le 2$
$\begin{array}{c}\mathit{P}\left(0\right)=2\\ \mathit{P}\left(\mathit{t}\right)=-1\end{array}\}$One real root lies between 0 & 1
One real root lies between 3 & 4
P(x) has only two real roots.
One real root lies in (0, 1) and One real root lies is (3, 4)