Roots of Polynomials (Edexcel A Level Further Maths: Core Pure)

The roots of the equation

are and 

Without solving the equation, find the value of

(i)   

(ii)   

(iii)   

where and  are real constants.

Given that  is a root of the equation 

show all the roots of on a single Argand diagram,

The roots of the equation

are  and .
Without solving the equation, find the value of

(i)   

(ii)   

(iii)