The quadratic polynomial depends on the real parameter .

MATHEMATICS · Multi-part · A Level · Mathematics · Algebra and Functions · Algebra and Functions

Problem

The quadratic polynomial

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

depends on the real parameter

m

. (i) Find the discriminant of the quadratic equation

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

in terms of

m

. (ii) Determine all integer values of

m

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

m

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