Question

Let $P\left(x\right)=x^{32}-x^{25}+x^{18}-x^{11}+x^4-x^3+1$. Which of the following are CORRECT?

• A. Number of real roots of $P\left(x\right)=0$ are zero
• B. Number of imaginary roots of $P\left(x\right)=0$ are $32$
• C. Number of negative roots of $P\left(x\right)=0$ are zero
• D. Number of imaginary roots of $P\left(x\right)+P(-x)=0$ are $32$

Answer 1

Answer: (A), (C), (D)

The correct options are
A Number of real roots of $P\left(x\right)=0$ are zero
C Number of negative roots of $P\left(x\right)=0$ are zero
D Number of imaginary roots of $P\left(x\right)+P(-x)=0$ are $32$