Most Important Selected Qs for JEE AdvancedMathematicsQuadratic Equation

If is a real root of the equation x^5-x^3+x-2=0 , then find the value of [ ^6 ] . [Note: [ ] ] denotes the greatest integer function.]

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Step-by-step solution

Let aligned f(x) & =x^5-x^3+x-2 f^ (x) & =5 x^4-3 x^2+1>0 x R aligned f(x) is increasing only one real root. f(1)=-1, f(2)=24 1 1 . aligned g(1) & < g( ) < g(2) 3 & < g( ) < 4 3 & < ^6 < 4 [ ^6 ] & =3 aligned [ ^6 ]=3

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