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

Answer: (B)

$f'(x)>0 \forall x \in R$
$f(x)=0$ has exactly one real root