Consider the quadratic equation

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

Problem

2x^2 + (k-5)x + k = 0

, where

k

is a real parameter. (i) Derive the expression for the discriminant

D

in terms of

k

. (ii) Find the set of all real values of

k

for which the equation has two distinct real roots. (iii) Determine the value(s) of

k

for which the equation has equal real roots. (iv) Find the set of all real values of

k

for which the equation has no real roots.