One positive root Case-2 −1≤x<0 −x2−2x−5x−5−1=0 x2+7x+6=0 (x+6)(x+1)=0 x=−1 one root in range Case-3 −2≤x<−1 x2−2x+5x+5−1=0 x2−3x−4=0 (x−4)(x+1)=0 No root in range Case-4 x<−2 x2+7x+4=0 x=
−7±√49−16
2
=
7±√33
2
one root in range Total number of distinct roots are 3