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The number of distinct real roots of the equation: x^4-4x^3+12x^2+x-1=0 , is

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Solution:   Put    f(x)=x^4-4x^3+12x^2+x-1   ..........(1)

                   ecause        f(-1)> 0 and f(0)< 0  Rightarrow   f(x)=0 has a real root in (-1,0)

                   ecause       f(0)< 0    and   f(1)> 0  Rightarrow  f(x) has a real root in  (0,1)

                  	herefore       No. of real roots is two.

                    Note that the other two roots are  imaginary.

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Deependra Verma

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