`|((1+alpha)^2,(1+ 2alpha)^2, (1+3alpha)^2),((2+alpha)^2,(2+ 2alpha)^2, (2+3alpha)^2),((3+alpha)^2,(3+ 2alpha)^2, (3+3alpha)^2)| =-648alpha` FInd the value of `alpha`

Which of the following values of alpha satisfying the equation |{:((1+alpha)^2,(1+2alpha)^2,(1+3alpha)^2),((2+alpha)^2,(2+2alpha)^2,(2+3alpha)^2),((3+alpha)^2,(3+2alpha)^2,(3+3alpha)^2):}|=-648alpha?

|[(1+alpha)^(2),(1+2 alpha)^(2),(1+3 alpha)^(2)(2+alpha)^(2),(2+2 alpha)^(2),(2+3 alpha)^(2)(3+alpha)^(2),(3+2 alpha)^(2),(3+3 alpha)^(2) Find the value of alpha

Which of the following values of alpha satisfying the equation |(1+alpha)^2(1+2alpha)^2(1+3alpha)^2(2+alpha)^2(2+2alpha)^2(2+3alpha)^2(3+alpha)^2(3+2alpha)^2(3+3alpha)^2|=-648alpha? -4 b. 9 c. -9 d. 4

Which of the following values of alpha satisfying the equation |(1+alpha)^2(1+2alpha)^2(1+3alpha)^2(2+alpha)^2(2+2alpha)^2(2+3alpha)^2(3+alpha)^2(3+2alpha)^2(3+3alpha)^2|=-648alpha? -4 b. 9 c. -9 d. 4

Which of the following values of alpha satisfying the equation |(1+alpha)^2(1+2alpha)^2(1+3alpha)^2(2+alpha)^2(2+2alpha)^2(2+3alpha)^2(3+alpha)^2(3+2alpha)^2(3+3alpha)^2|=-648alpha? -4 b. 9 c. -9 d. 4

Which of the following values of alpha satisfying the equation |(1+alpha)^2(1+2alpha)^2(1+3alpha)^2(2+alpha)^2(2+2alpha)^2(2+3alpha)^2(3+alpha)^2(3+2alpha)^2(3+3alpha)^2|=-648alpha? -4 b. 9 c. -9 d. 4

Which of the following values of alpha satisfying the equation |(1+alpha)^2(1+2alpha)^2(1+3alpha)^2(2+alpha)^2(2+2alpha)^2(2+3alpha)^2(3+alpha)^2(3+2alpha)^2(3+3alpha)^2|=-648alpha? -4 b. 9 c. -9 d. 4

If f(alpha) = |{:(1,alpha,alpha^2),(alpha,alpha^2,1),(alpha^2,1,alpha):}| , then find the value of f(3^(1/3)) .

Prove that |{: (1,alpha,alpha^2), (alpha,alpha^2, 1),(alpha^2, 1,alpha) :}|=-(1-alpha^3)^2

alpha=e^((2 pi)/(5)i)then1+alpha+alpha^(2)+alpha^(3)+alpha^(4)+2 alpha^(5)=