WBJEE · Maths · Quadratic Equation
Let \(f(x)=x^{13}+x^{11}+x^{9}+x^{7}+x^{5}+x^{3}+x+12\). Then
- A \(f(x)\) has 13 non-zero real roots
- B \(\mathrm{f}(\mathrm{x})\) has exactly one real root
- C \(\mathrm{f}(\mathrm{x})\) has exactly one pair of imaginary roots
- D \(f(x)\) has no real root
Answer & Solution
Correct Answer
(B) \(\mathrm{f}(\mathrm{x})\) has exactly one real root
Step-by-step Solution
Detailed explanation
Hint: \(f^{\prime}(x)>0 \quad \forall x \in R\) \(f(x)=0\) has exactly one real root
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