Answer to Question #104049 in Calculus for Akshay Kumar

Question

Find the nature of the roots of the polynomial
2X5+ X³+ 5X+ 1

Answer 1

The degreee of this polynomial is n=5. Since all of the coefficients for the plynomial are real, and it's degree is odd, the pilynomial will have at least one real root.

Drawing th plot of the polynomial will show us, that there is only one real root.

Therefore, all of the other roots would be two pairs of conjugate complex numbers.