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  • If the zeroes of the cubic polynomial x^3+3x^2+kx-3 are alpha-beta,alpha,alpha+beta then find the value of alpha,beta and k. plz help me with this.(alpha=-1,beta=+_2,k=-1?

If the zeroes of the cubic polynomial x^3+3x^2+kx-3 are alpha-beta,alpha,alpha+beta then find the value of alpha,beta and k. plz help me with this.(alpha=-1,beta=+_2,k=-1?

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alpha-eta,;alpha,;alpha+eta;are;the;zeroes;of;cubic;polynomial; x^3+3x^2+kx-3\*Rightarrow sum;of;zeroes=-fracba=-frac(-3)1=alpha-eta+alpha+alpha+eta=3\*Rightarrow 3alpha=3Rightarrow alpha =1\* product;of;zeroes=frac-da=-frac(-3)1=(alpha-eta) imes alpha imes (alpha+eta)=3\* Rightarrow (alpha^2-eta^2) imes alpha=3\* Now,;put;alpha=1\* Rightarrow (1-eta^2) imes 1=3\*Rightarrow 1-eta^2=3\*Rightarrow eta^2=-2Rightarrow eta =pmsqrt2iota \* sum;of;products;of;zeroes=(alpha-eta)(alpha)+(alpha)(alpha+eta)+(alpha+eta)(alpha-eta)\*Rightarrow sum;of;products;of;zeroes=fracca=frack1=k\*Rightarrow k=3alpha^2-eta^2\* Rightarrow k=3(1)-(-2)=3+2=5\* So,;alpha=1,;eta=pmsqrt2iota;and;k=5

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Deependra Verma

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