Mathematics

Problem

The quadratic polynomial

x^2 + (2m-3)x + m^2 - 4

depends on the real parameter

m

. a. (i) Find the discriminant of the quadratic equation

x^2 + (2m-3)x + m^2 - 4 = 0

in terms of

m

. b. (ii) Determine all integer values of

m

for which the equation has rational roots. c. (iii) For each value of

m

found in part (ii), obtain the roots and write the polynomial in its factorised form.