GATE Electrical Engineering (EE) 2021 Solved Papers

Number of real (+ve) roots ≤ Number of sign changes in p(x)=2
Number of real (−ve) rots ≤ Number of sign changes in p(−x)=0
So, p(x)=0 has no (−ve) real roots and a maximum of 2(+ve) real roots
∴ Number of real roots of ' P(x)=0′≤2

P(0)=2

P(t)=−1

}One real root lies between 0 & 1

P(3)=81−108+2<0

P(4)=256−256+2>0

}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)