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  • The number of distinct real roots of the equation  is </p

The number of distinct real roots of the equation \mathrm{x^{7}-7x-2=0} is 

Option: 1

5


Option: 2

7


Option: 3

1


Option: 4

3


Answers (1)

best_answer

\mathrm{x^{7}-7 x-2=0 }

let \mathrm{ f(x)=x^{7}-7 x-2}\\

\mathrm{ f^{\prime}(x)=7\left(x^{6}-1\right)=7\left(x^{3}-1\right)\left(x^{3}+1\right)} \\

\mathrm{ =7(x-1)(x+1)\left(x^{2}+x+1\right)\left(x^{2}-x+1\right)}

at \mathrm{x=1; f(x)=1+7-2=-8}  , \mathrm{x=-1; f(x)=-1+7-2=4}

Hence 3 distinct solutions

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Sayak

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