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  • For the equation 3x^2+px+3=0 p>0 , if one of the roots is square of the other , then p is equal to

For the equation 3x^2+px+3=0 p>0 , if one of the roots is square of the other , then p is equal to

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Solution:  Let alpha ,alpha ^2 be the roots of 3x^2+px+3=0

Then  alpha +alpha ^2=-p/3;and;alpha imes alpha ^2=1

As alpha ^3=1 , we getalpha =1,omega ;or;omega ^2

If alpha =1;then;p=-3(alpha +alpha ^2)=-6<0

Not possible as p>0

We take  alpha =omega ;and;alpha ^2=omega ^2 , so that -p/3=omega +omega ^2=-1Rightarrow p=3

Posted by

Deependra Verma

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