Question

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) \(f(x)\) has exactly one real root
(C) \(f(x)\) has exactly one pair of imaginary roots
(D) \(f(x)\) has no real root

Answer 1

Ans: (B)
Hint : \(f^{\prime}(x)>0 \quad \forall x \in R\)
\(f(x)=0\) has exactly one real root