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Functions — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsFunctions2 Marks
MCQ
The equation $x^3+x-1=0$ has
  • A
    no real root.
  • B
    exactly two real roots.
  • ✓
    exactly one real roots.
  • D
    more than two real roots.
✓

Answer

Correct option: C.
exactly one real roots.
(c) : $f(x)=x^3+x-1$ Now, $f(0)=0+0-1=-1<0$ and $f(1)=1+1-1=1>0$ So, $f(x)$ has a root in between 0 and 1 and $f^{\prime}(x)>0 \in R \forall$ $x>1 \therefore f(x)$ has exactly one real root.

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