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Question

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

A
x6+4x3+5
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B
x16+24x3
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C
x99+1
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D
x1001
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Solution

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

The degree of the polynomial x6+4x3+5 is 6.
The degree of the polynomial x16+24x3 is 16.
The degree of the polynomial x99+1 is 99.
The degree of the polynomial x1001 is 100.
Hence, the polynomials arranged in ascending order according to their number of zeros is:
x6+4x3+5
x16+24x3
x99+1
x1001

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