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If the roots of the cubic equation x^(3...

If the roots of the cubic equation ` x^(3) -9x^(2) +a=0 ` are in A.P., Then find one of roots and a

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Let `alpha -beta, alpha, alpha +beta` be roots of the given equation ` x^(3) -9x^(2) + a=0` then
` alpha - beta alpha +alpha + beta =9`
` Rightarrow alpha =3 `
One of roots of the given equation is 3. substituting x=3, we get
27 - 81 +a =0
a= 54
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