WBJEE · Maths · Application of Derivatives
Let \(p(x)\) be a polynomial with real co-efficients, \(p(0)=1\) and \(p^{\prime}(x) > 0\) for all \(x \in \mathbb{R}\). Then
- A \(p(x)\) has at least two real roots
- B \(p(x)\) has only one positive real root
- C \(\mathrm{p}(\mathrm{x})\) may have negative real root
- D \(p(x)\) has infinitely many real roots
Answer & Solution
Correct Answer
(C) \(\mathrm{p}(\mathrm{x})\) may have negative real root
Step-by-step Solution
Detailed explanation
\(P(x)=0\) has exactly one negative real root.
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