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MHT CET20239 May 2023Evening ShiftMathematicsApplication of DerivativesActual

The equation x^3+x-1=0 has

Options

  1. Ano real root.
  2. Bexactly two real roots.
  3. Cexactly one real root.
  4. Dall three real roots.

Correct answer

C. exactly one real root.

Step-by-step solution

Given equation x^3+x-1=0 Let f (x)=x^3+x-1 array ll & f ^ (x)=3 x^2+1 & f ^ (x)>0 x R array f (x) is increasing for x₂>x₁, f (x₂ )> f (x₁ ) Now, f (0)=-1 and f (1)=1 f (x)=0 for some x (0,1) Equation has one real root.

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