1.Let a be the common root of the two equations x^2+bx+c=0 and x^2+cx+b=0, where b and c are distinct rational numbers.
(a) Find the value of a.
(b) Suppose 3b and 3c are the roots of the equation x^2+3px+q=0 .......(*), where p and q are positive integers.
(i) Find the value of p.
(ii) By considering the discriminant of (*), or otherwise, determine the value of q.