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Grade 12th PassAlgebra

if a+ib is a root of x^3 +qx +r=0;q,r belongs to R...

then a real cubic eqn independent of a and b whose one root is 2a is...

abhinav ...

13 Years agoGrade 12th Pass

1 Answer

Arun Kumar

12 Years ago

Hi
$\\x^3 +qx +r=0 \\$since a+ib is root$ \\=>$a-ib is root too$ \\=>a+ib+a-ib+root_3=0 \\=>root_3=-2a \\$if we want one root to be 2a $=>$ change signs of other root too$ \\=>\sum roots =0 $ still$ \\=>\sum root_1*root2=$same as before because its negative * negative = +$ \\=> \prod roots=-r $ because - multiplied 3 times$ \\required equation \\x^3 +qx -r=0$
Thanks & Regards, Arun Kumar, Btech,IIT Delhi, Askiitians Faculty

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