HKAL Pure Mathematics Past Paper Topic: Polynomials
25. (96I11) Suppose the equation x4 3x2 k 0 ……… (*) has two roots , such that + = 2 .
(a) Show that . (5 marks) (b) Show that 2 , 2 are two distinct roots of the equation
y2 3y k 0 . Hence find the value of k . (5 marks) (c) Solve (*) and express the roots in the form
a b where a ,
b are rationals. Hence find the values of and . (5 marks)
P. 22