Question

Let $f\left(x\right)=x^{13}+x^{11}+x^9+x^7+x^5+x^3+x+19.$ Then $f\left(x\right)=0$ has

• A. $13$ real roots
• B. only one positive and only two negative real roots
  
• C. not more than one real root
• D. has two positive and one negative real root

Answer 1

The correct option is C not more than one real root

$f^{\prime }\left(x\right)=12x^{12}+11x^{10}+9x^8+7x^6+5x^4+3x^2+1>0\forall x\in R$
So $f\left(x\right)$ is an increasing function and power is odd there will be exactly one real root