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musickatia [10]
3 years ago
7

Explain the difference between finding rational zeros and finding all zeros.

Mathematics
1 answer:
r-ruslan [8.4K]3 years ago
8 0

Answer:

see explanation

Step-by-step explanation:

Given the polynomial

p(x)=a_nx^n+a_{n-1}x^{n-1}+a_{n-2}x^{n-2}+...+a_2x^2+a_1x+a_o

The rational zeros are all the possible factors of a_0 dived by all the possible factors of a_n. Therefore we use the rational rots theorem to find all possible rational zeros.

To find all zeros we use the remainder theorem. Thus, we plug in all the rational zeros to determine which ones evaluate to zero. These are the real zeros. We could also use long division to find the remaining zeros as soon as we got the first zero with the remainder theorem.

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