Let f(x)=x13+x11+x9+x7+x5+x3+x+12. Then

Question

Let f(x)=x13+x11+x9+x7+x5+x3+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

Tardigrade Admin · Accepted Answer

f'(x)>0 ∀ x ∈ R f(x)=0 has exactly one real root

Q. Let $f (x) = x^{13} + x^{11} + x^{9} + x^{7} + x^{5} + x^{3} + x + 12$ . Then

$f (x)$ has 13 non-zero real roots

$f (x)$ has exactly one real root

$f (x)$ has exactly one pair of imaginary roots

$f (x)$ has no real root

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

Q. Let f(x)=x13+x11+x9+x7+x5+x3+x+12. Then

f(x) has 13 non-zero real roots

f(x) has exactly one real root

f(x) has exactly one pair of imaginary roots

f(x) has no real root