A.Maths question

Let the common root be y
∴y2+ay+b=0 and y2+py+q=0
∴ay+b=py+q
(a-p)y=q-b
y=(q-b)/(a-p)
∴[(q-b)/(a-p)]2+a[(q-b)/(a-p)]+b=0
(q-b)2+a(q-b)(a-p)+b(a-p)2=0
a(q-b)(a-p)+b(a-p)2=-(q-b)2
(a-p)[a(q-b)+b(a-p)]=-(b-q)2
(a-p)(aq-bp)=-(b-q)2
(a-p)(bp-aq)=(b-q)2

唔．．．真是一個匪夷所思的方法~
我是
suppose root for first equation is alpha and beta,
then a = - (alpha + beta) , b = alpha * beta
suppose root for second eqn is alpha and gamma,
then p = - (alpha + gamma) , q = alpha*gamma
全部 expand，再對番左右....　太笨了>3<"

x^2 + ax + b = 0......................(1)
x^2 + px + q = 0.......................(2)
(1) - (2) we get
ax -px = -b + q, therefore, x = (q-b)/(a-p).....................(3)
p x (1) - a x (2) , we get
px^2 + apx + bp -ax^2 - apx - aq = 0
(p-a)x^2 = aq -bp............(4)
Substitute (3) into (4)
(p-a)[(q-b)/(a-p)]^2 = aq - bp
(q-b)^2/(p-a) = aq- bp, therefore,
(b-q)^2 = (aq-bp)(p-a) = (a-p)(bp-aq).