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  • Irrational roots of the equation 2x^4+9x^3+8x^2+9x+2=0 are

Irrational roots of the equation 2x^4+9x^3+8x^2+9x+2=0 are

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Solution:  Divide the given equation by x^2 to obtain

                 2(x^2+1/x^2)+9(x+1/x)+8=0

               Put ,     x+1/x=t to get 2(t^2-2)+9t+8=0

               Rightarrow     t=-1/2,-4

                herefore   x+1/x=-1/2,-4

               Rightarrow    x^2+1/x=-1/2  ,   x^2+1 /x=-4

               Rightarrow    2x^2+x+2=0   ,x^2+4x+1=0

              The first equation has non real complex roots

           and the second equation has irrational roots .   -2pm sqrt3.

 

Posted by

Deependra Verma

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