Let (m+1)x2−2(2m−3)x+(m−4)=0 be a quadratic equation in x, where m is a real parameter.
a. (i) Find the condition on m for which the equation has real roots.
b. (ii) Further, obtain the range of m for which the two real roots are of opposite signs.
c. (iii) For the value(s) of m found in part (ii), calculate the product of the roots.