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Grade: 11
        
let alpha,bita be the root of ax2+bx+c=0(a≠0)and gama,sigma be the roots of px2+qx+r=0(p≠0),and
D1,D2 be the respective discriminants of these equations.If alpha,bita,gama,sigma are in A.P.,then D1:D2 equals
one year ago

Answers : (1)

Aditya Gupta
1816 Points
							
answer is a^2/p^2.
simply note that (x-an)(x-an+1)= x-(an+an+1)+anan+1 has a discriminant of d^2 where d is the common difference
now write  ax2+bx+c=0 as  x2+bx/a+c/a=0 and px2+qx+r=0 as x2+qx/p+r/p=0 so that the discriminant of bothTHESE eqns is d^2 each. 
or (b/a)^2 – 4c/a= (q/p)^2 – 4r/p
and from here we obtain 
D1:D2 = a^2/p^2
one year ago
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