If alpha is a root of 4x^2+2x-1 =0 . prove that 4(alpha)^3- 3(alpha) is the other root.

Answers (1)

Solution:   Let other root is eta , then 

                                       alpha+eta =-frac24=-frac12Rightarrow eta=-frac12-alpha

   and  so , 4(alpha)^2+2(alpha)-1=0,  because alpha is a root 4x^2+2x-1=0

   Now ,                   eta=4(alpha)^3-3(alpha)=alpha(1-2alpha-3)=-frac12-alpha

  Hence   ,  4(alpha)^3-3(alpha)  is the other root.              

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