Question

Arrange the following polynomials in ascending order of the maximum number of zeros they can have.

• A. $x^6+4x^3+5$
• B. $x^{16}+24x^3$
• C. $x^{99}+1$
• D. $x^{100}-1$

Answer 1

The maximum number of zeroes, a polynomial can have is equal to the degree of the polynomial.

The degree of the polynomial $x^6+4x^3+5$ is 6.
The degree of the polynomial $x^{16}+24x^3$ is 16.
The degree of the polynomial $x^{99}+1$ is 99.
The degree of the polynomial $x^{100}-1$ is 100.
Hence, the polynomials arranged in ascending order according to their number of zeros is:
$x^6+4x^3+5$
$x^{16}+24x^3$
$x^{99}+1$
$x^{100}-1$