If 3 lines in between the roots of the equation x^2+2mx+9=0,then m must bee in the interval?

Hello student,
Please find the answer to your question below
Givenlie s in between the roots of the equation x^2+2mx+9=0
So f(3)<0 hence we get9+6m+9<0 so m<-3..........(1)
also as product of roots is +ve both must be positive or both must be -ve
as 3 lies between the roots of the eqn both the roots must be +ve
so discriminant>=0
4m²-36>=0
(m+3)(m-3)>=0
m(-,-3]u[3,).........(2)
From 1 and 2 we get m(-,-3)