A.Maths一問 (20分)

Q: If @and B are the roots of the quadratic equation ax^2+bx+c=0, prove that a quadratic equation with roots @^2 and B^2 is a^2(x^2)-(b^2-2ac)x+c^2=0.

A: Given @ and B are roots of ax^2+bx+c=0
Sum of the roots=@+B= -b/a
Product of the roots=@B= c/a
.'. @^2+B^2= (@+B)^2-2(@B)
= (b^2)/(a^2) - (2c)/(a)
= [1/(a^2)](b^2-2ac)
@^2(B^2)= (c^2)/(a^2)
A quadratic equation with roots @^2 and B^2 is
x^2-[1/(a^2)](b^2-2ac)x+(c^2)/(a^2)=0
(a^2)x^2-(b^2-2ac)x+(c^2)=0

我想問點解要x^2-[1/(a^2)](b^2-2ac)x+(c^2)/(a^2)=0?
[1/(a^2)](b^2-2ac)同(c^2)/(a^2)唔係個product of roots & sum of roots meh?
點解要加左入quadratic equation?????