Question

Given that the quadratic equation is (2m+3)x^2+(4m-2)x-(m+1)=0.Find the value of m,if

•one of the root of the equation is negative

•one of the root of the equation is reciprocal of the other

Answer 1

the roots are

x = -[(2m-1)±√(6m^2+m+4)]/(2m+3)

The product of the roots is

-(m+1)/(2m+3)
If that is negative, then
(m+1)>0 and (2m+3)>0, so m > -1
(m+1)<0 and (2m+3)<0, so m < -3/2

If the roots are reciprocals, then
-(m+1) = 2m+3
3m = -4
m = -4/3