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ajinkya bhole Grade: 10
        


if x3+px+q=0 has two equal roots then show that 27q2+4p3=0



 


 


 


 


 


 


 


 


 


 


 


 


 


 


 


 


 


 

7 years ago

Answers : (2)

AskiitiansExpert Abhinav Batra
25 Points
										

dear ajinkya


suppose α is the double root of x3+px+q=0


then sum of roots of x3+px+q=0 is given by -1* coefficient of x2


let β be the thir root of the given equation


then 2α+β=coefficien -1*0=0


so β=-2α


Double   sum of roots of x3+px+q=0 is given by coefficient of x


so α2 +αβ+βα=p


But β=-2α


so α2 -4α2=p


-3α2 =p 


-108α6=4p3-----1


Product of roots of given equation is given by -1*constant term


so   α2 *-2α=-q


     2α3=q 


    108α6=27q2---2


Adding eq 1 and eq 2


4p3 + 27q2=0






ALL THE best


AskIITIANsExpert


ABhinav Batra















7 years ago
soumyabrata pal
18 Points
										

Let  the roots be x,x,y.


then 2x+y=0


x2 +xy+xy=p


or p=x(x+2y)


or p=x(x-4x)


or p=-3x2


or p3=-27x6


also


x4y2 =q2


or q6=4x6


hence 4p3+27q3=0


proved

7 years ago
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