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Question: Answered & Verified by Expert
Let $a$ and $b$ be two distinct roots of a polynomial equation $f(x)=0$. Then there exists at least one root lying between $a$ and $b$ of the polynomial equation.
MathematicsApplication of DerivativesNDANDA 2009 (Phase 1)
Options:
  • A $f(x)=0$
  • B $f^{\prime}(x)=0$
  • C $f^{\prime \prime}(x)=0$
  • D None of these
Solution:
1316 Upvotes Verified Answer
The correct answer is: $f^{\prime}(x)=0$
Rolle's theorem says between any two roots of a polynomial $f(x)$, there is always a root of its derivative $f^{\prime}(x)$
Therefore between $a$ and $b$. There exist at least one root of the polynomial equation $f^{\prime}(x)=0$

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