[Fint the k1 range that system is stable]

hello ,Guys , I have a question that this book.

I am confused the K1 range value

on step for solved the quadratic formula. the book is get root for K1=-4.865 & 25.87. that is correct.

So i return the quadratic formula that is (K1+4.865)(K1-25.87) and then the fornula need positive,

So the quadratic formula must be (K1+4.865)(K1-25.87)>0 , and then the value should K125.87.

that is fully the formula , but why does book written the range is -4.865

is book written wrong? please help me my confused.

SOLUTION: The first step is to reduce the pitch control system to a single, closed-loop transfer function. The equivalent forward transfer function, Ge(s), is 0.25K1(s +0.435) s4 3.456s3 3.457s2 +0.719s 0.0416 Ge(s) (6.37) With unity feedback the closed-loop transfer function, T(s), is 0.25K1(s +0.435) s4 3.456s3 3.457s2 (0.719 + 0.25K1)s +(0.0416 0.109K1) The denominator of Eq. (6.38) is now used to form the Routh table shown as Table 6.20. (6.38) TABLE 6.20 Routh table for UFSS case study 4 3.457 0.719 + 0.25K1 0.144 +0.377K1 0.0416 + 0.109Ki 3.456 11.228 - 0.25K1 0.0625K +1.324K1 7.575 11.228 - 0.25K1 0.144 + 0.377K, 0