The quadratic equation (k+1)x2+(2k−3)x+(k−4)=0 depends on the real parameter k.
(a) Find the condition on k that ensures the equation has real roots.
(b) Using the additional requirement that the two roots are of opposite signs, determine the set of all real values of k satisfying both conditions.
(c) For one value of k obtained in part (b), verify explicitly that the product of the roots is negative.