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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

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  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

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